( ) ± = 2018

Transcription

1 30 ( 3 ) ( ) 2018

2 ( ) ± = 2018

3 (PDF ), PDF PDF. PDF, ( ), ( ),,,,., PDF,,.

4 , 7., 14 (SSH).,,,.,,,.,., ,,. 3.,,. 4...,, 14 16, 17 21, 22 26, 27( ), SSH,,,, ( 7 9 ), ( SSH ), ( 17 21, 22 26, 27 SSH ),,,. 2,,,., 2.,,. 1, 2,. 30 4

5 1. 2.

6 i ( )

7 ii SI ( ) SI ( ) sin cos , a = b

8 iii ( ) ,? ( )

9 iv ,

10 ,.,,.,,,, = 5., 6,..,, 2 a, 1 b, 3 c, 5 d,. b a d c = b d a c = b d a c,., a+3 b 2 x 2,. a b ( ),,.,. 3 2 a, y 5 x 3 x 2, y 5

11 = 2., = = 2 25,.,,. b a d c = b a c d = b c a d,,. b a d c = b a d c = b c a d (b c),, (a d).,,,.. b a d c b a d c = b d a c = b d a c = b a c d = b c a d, b a d c = b a d c = b c a d 1.. (,,,.) (1) (5) a b 2 b c a (2) (6) b a x 2 (3) a c y b 1 a 1 b (7) (4) x a 2 b c y x w z y a c

12 = 4., 5,..,,.,. b a + c a = b + c a b a c a = b c a, = 7 6., = = = 7 6.,,,., 1 2 3, 2 3 6, 6 2, , 2.,,.,.,,, b a + d c = b a c c + d c a a = b c a c + a d a c b a d c = b a c c d c a a = b c a c a d a c = b c + a d a c = b c a d a c. a c,.

13 4 1 (1) b a + c a = b + c a b a c a = b c a (2) b a + d c = b a c c + d c a a = b c a c + a d a c = b c + a d a c b a d c = b a c c d c a a = b c a c a d a c = b c a d a c 2.. (1) (4) (7) h g j i 2 a b c x 2 1 (2) (5) 1 x x b c a x 2 (8) (3) (6) 1 3 a b a 2 b q p + s r 1 a a 1 1.2, 1., x w = z y, x, x =., x w, w, x w w = z y w, w, x, x =. x = = wz y z y w

14 1.2. 5, a =,.. b a = d c, a.., a, b., 2. 1, a b =. b a a = b = d c a a d c., d c a d c, d c c d. b c d = a d c, a.. 2 b c d = a a = b c d c d,, b. b a b = d c b b a 1 = d b c 1 b 1 a = d b c.,,,. a = b c d

15 6 1,,., 1 a = 1 b + 1 c,,,., 1 a = 1 b + 1 c = c b c + a = b c b + c b b c = b + c b c ( 1 ),,.,. 1 S 10 = 0 S = 5 2 x a + x b = 1 a c x + b x = c 3 b x + c b x = 2 b x + 2 c 3 b x + 5 = 2 x = a + x b a = 1 b + 1 c + 1 d x (b + 1) = a + x a = b c d b + c + d 3.. (1) I = V (I : [A], V : [V], R : [Ω]) R R =. I = 0.3 [A], V = 3 [V], R. (2) b x 3 = 4 x c x =. ( b c 1 ) (3) b x + 3 = c x b x =. ( b c )

16 (4) b x 3 = 4 c x c (5) 3 x a (3 x + c) = (6) b c = (7) a x = 1 x + 1 x 2 a x x =. ( b 1 ) 4 b 4 a b c x =. ( c 0) x =. ( b c ) x =. ( a 0 ) 1.3, x =. x 2 = 1 (x > 0) 3 1, x =., x 2 3,.,, a 2 = c b (a > 0, b > 0, c > 0). c a 2 = b c a = b, x =. x 2 = 3, x = 12., ( : ), 2.,, a = 2, b = 3, c = x a = c b (a > 0, b > 0, c > 0)

17 8 1. c., 2 a 2 = c b, b a 2 b = c b b a 2 b = c c = a 2 b. a, b, c x = = 12. 2,. a 2 = c b a = c b ( a > 0, b > 0, c > 0), 2. a = c b a 2 = c b ( a > 0, b > 0, c > 0) ( 2 ),,.,. x = 4 x + 3 = 2 v 2 = 2 g h + v 0 2 v = 2 g h + v (1) x 2 = 1 4 x. ( x > 0 ) (2) 10 = 5 x x.

18 (3) 3 = x 5 x. (4) y 2 = x + 3, x =. (5) y = c x, x =. ( c 0 ) (6) y = (7) z x 1 x 1, x =. ( y 0 ) = 2 x. (8) x 2 = 1 y, x =. ( x > 0, y > 0, z > 0 ) z2 (9) f = 1 2π LC, C =. ( f 0 ) y. x = 2 1 y = x y = 5., x = 2 2 x 1 y = y = 5., x = t y = t + a (a ) y = x + a., y t. 2, x, y, t 3.,, x, y, 2 t.

19 x y, t, t y x. x = t 1 1 y = 2 t + 3 2, 1 t =. t = x + 1 1, 1 2 t. y = 2 (x + 1) + 3 y = 2x y = 2x (1) 2 t, y, x. x = 2 t y = 4 t (2) 2 t, y, x. ( a, b, a 0 ) x = a t y = b t (3) 2 t, y, v. ( g, g 0 ) v = g t y = 1 2 g t2 (4) 2 t, y, x. x = 2 t 1 y = 4 t t + 3 (5) 2 t, y, x. ( a, b ) x = t a y = 3 t + b

20 ,.,. 1 1, R 1 [Ω] R 2 [Ω], E [V]., , R 1 [Ω] R 2 [Ω], 1 1 R 1 [Ω] R 2 [Ω] 1 ( ) R [Ω], R [Ω] R 1 [Ω], R 2 [Ω],. 1 R = 1 R R 2,. 1 1, I 1 = E R 1 1, I 2 = E R 2 2. I [A], ( ), I = I 1 + I 2 3

21 12 1, 3 1, 2, E I = + E R 1 R 2 ( 1 = E + 1 R 1 R 2 ) 4., 1 1,, I = E R 5. 4 I [A] 5 I [A], 4 5 E R ( 1 = E + 1 R 1 R 2 ) 6 1, 6 E ( E ) E R 1 ( 1 E = E + 1 ) 1 R 1 R 2 E, 1 R = 1 R R 2 7., 7 R =, R = R 1 R 2 R 1 + R (1) 1 1, R 1 = 20 [Ω], R 2 = 30 [Ω], R. (2) 7, 8. (1),. (3) 1 1, R 1 = a [Ω], R 2 = 2 a [Ω], R.

22 , 3 R 1, R 2, R 3, E [V]. 1.5,. (1) R 1 I 1, E, R 1., I 2 E, R 2,, I 3 E, R 3,. (2) I, I 1, I 2, I 3. (3) R, I, E, R. (4) (2), (1). (5) (3) (4), R [Ω] R 1 [Ω], R 2 [Ω], R 3 [Ω],. ( 1 R =. ) (6) R 1 = 10 [Ω], R 2 = 15 [Ω], R 3 = 30 [Ω], R. (7) R 1 = a [Ω], R 2 = b [Ω], R 3 = 3 b [Ω], R.

23 (1) 1 a = 1 b + 1 c + 1 d a =. (2) P V = w M (3) (4) 1 a + 1 b = 1 f 4 b x + c = 2 b x + c R T M =. b =. ( P 0, V 0 ) x =. ( b 0 ) x (5) a + 2 = x =. ( a 1 ) b + x l 2. T = 2π g =. ( T 0 ) g 3. v > 0, F x = 1 2 m v2 v = W = 1 2 Q V 1 ( F > 0, x > 0, m > 0 ) Q = C V 2,. (1) W C, V. (2) W C, Q. ( C 0 ) 5. 2 M a = M g T m a = T m g 1 2 ( M > m > 0 ),. (1) a M, m, g. (2) T M, m, g.

24 15 2,, ( : = , = ).,,. 2.1 a n a n, a n. a a = a 2, = 2 3, X X X X = X 4., a 1, a 2, a 3, a 4, a ( ), a ( ), a 1, 2, 3, 4,. 2, 3, = = = = = = = = = = = = = = =

25 16 2 m, n (1) a m a n = a m+n (2) a m a n = (3) (a m ) n = a m n (4) (a b) n = a n b n a m n (m > n) 1 (m = n) a 0 1 a n m (m < n) (5) ( b a ) n = bn a n a 0 (1) (5),. (1) a m a n = m n {}}{{}}{} a a {{ a a a } m + n = a m+n = = 3 6 = = = = 4 5 = 1024 (2) 1 m > n a m a n = 2 m = n am a n = = m {}}{ a a a a a }{{} n n m n {}}{{}}{ a a a a a } {{ a } n a m a n = m {}}{ a a a a a a }{{} m = m n {}}{ a a = a m n = 1

26 m = n, 1,. a m n = a m m = a 0 = 1 a 0 = = = 5 0 = 1, = = 10 0 = 1 3 m < n a m a n = m {}}{ a a a a } a {{ a } a } {{ a } m n m = 1 a n m 1 a m n 1 = a n m, m = 0, a 0 n 1 = a n 0, a n = 1 a n. a 1 = 1 a, a 3 = 1 a 3., m, n = = = 1 4 ( ) = = 2 2 = = = = = ( ) = = 10 3 = = a a 4 = 1 a 4 1 = 1 a 3 ( ) a a 4 = a 1 4 = a 3 = 1 a 3 (3) m m m (a m ) n {}}{{}}{{}}{ = ( a a) ( a a) ( a a) }{{} m n (m n ) = a m n 4. (a 3 ) 2 = a 3 2 = a 6 (10 2 ) 2 = = 10 4 = (2 4 ) 2 = = 2 8 = 256

27 18 2 (4) (a b) n = n {}}{ (a b) (a b) (a b) = (a } a {{ a } ) (b } b {{ } b) = a n b n n n 5. (2 3) 3 = = 8 27 = 216 (4 x 2 ) 2 = 4 2 (x 2 ) 2 = 4 2 x 2 2 = 16 x 4 (5) ( b a ) n = = n ({ ) ( )}} ( ){ b b b a a a n {}}{ b b b a a a }{{} n = bn a n 6. ( ) x 3 = x3 3 ( ) 3 a 2 = = x3 27 (3 a)2 4 2 = 9 a (1) (2) (6 2 ) 3 (3) (4) (5) (6) (7) (8) ( 3 4 ) 4 2. a, b, x, y 0,. (1) a 3 a (2) a 4 a 3 a 2 (3) a 2 a 5 (4) (a b 2 ) 3 (a 2 b) 2 (5) 4 x 2 (2 x y 3 ) 2 (6) 5 a 3 3 a 4 (7) 28 a 2 (7 a 3 ) (8) (a 4 ) 3 (9) (a 2 ) 3 (10) a 5 a 0 3. a, b, c, x, y 0,. (1) (4) a 3 a 3 (2) (a 3 ) 2 (a 4 ) 3 (3) (a 2 b 1 ) 2 a (6 x 2 y) 2 15 a 2 b 3 c 9 x 3 y 3 (5) ( 5 a b c 2 ) 2

28 a, b, c, x, y 0,. (1) 3 a 3 b 2 (2 a b 2 ) 3 6 a 3 b 2 (2) (2 x y 2 ) 3 6 x 4 y 2 (3) 60 a 2 7 b c 48 a3 c 3 35 b 3 ( ) 2 a c 2 2 (4) 5 b 2 (7 a 2 b) 2 21 x 3 y 3 3 x 2 y 35 (a b 2 ) 2 5. r, h. b2 a, a b, V, V. 2.3,,, = , = , x x = a 10 n ( 1 a < 10, n )., n x., (1) n 0, x n+1. (2) n, x n 0. ( n n ),,. 6. a 10 n ( 1 a < 10, n ). (1) 4470 (2) (3) (4) (5) , ( ). (1) (2) (3) (4) (5)

29 a 10 n ( 1 a < 10, n )., (2), (3), (4), a 2. (1) 20 4 = (2 10) 4 = = = = (2) = ( ) ( ) ( ) = ( ) = = ,,. (3) = ( ) ( ) = = = (4) = ( ) 3 = = = , 1. (1) (2) (3) (4) (5) ( ) 2 ( ) 2 (6) ( ) 3 ( ) [g], , 1.00 [g],., [g]

30 ( ),. A = ,.,, ( ), 3 ( ).., 3. 3, A = 3, 234, 589, 124.,, 3., 10 0 (one), 10 1 (ten), 10 2 (hundred), 10 3 (thousand : ), 10 6 (= , million : ), 10 9 (= , billion : ), 10 3, 3.,, 10 0 ( ), 10 1 ( ), 10 2 ( ), 10 3 ( ), 10 4 ( ) 10 8 (= : ), (= : )., 10 4, 4. A = 32, 3458, 9124, 2., A = (3 ) (4 ),.

31 ( ), 2 a, 3 a, a 2 ( ), a 3 ( ). n, n a a n. 2, 3, 4,,., 2 2 = 4, ( 2) 2 = , 2 3 = 8, ( 2) 3 = ( 1 ), ( 1 )., x 2 = 2, 2 2., a n,. a > 0 a < 0 n. n n., n n a., ( n a ) n = a. n = 2 2 a a = 9 = 3 2 = = = = 3 ( 2) 3 = = = (1) (4) 2 49 (2) 3 64 (3) 5 32 (5) 3 64 (6)

32 , n a,. ( n a ) n = a = a 1, (3) (a m ) n = a m n, n a = a 1 n., ( n ( ) a ) n = a 1 n 1 n = a n n = a 1 = a., a a m n a m = (a m ) 1 n = a m 1 n = a m n. a > 0, m, n, a 1 n = n a a m n = n a m,, = = , a m n. (1) 4 10 (2) 7 15 (3) (4) 3 16 (5) (6) [cm 3 ]. a [cm].

33 24 2 n a n a. nth root of a., a n., n, a, a n, a n,.,.,, n a.,.,,,,,.,,,,,,,., ,.

34 [mm] 1.00 [km],.,, ρ = [Ω m]. (, R [Ω], l [m], S [m 2 ].,,, R = ρ l S [Ω]. S = πr 2 [m 2 ], π = 3.14., 1 2.), 1.0 [mm],. 22 [Ω/km],, [mm],. 100 [Ω/km]. 2.., c = [m/s], l = [m] [g], , ρ = 8.93 [g/cm 3 ]. 1 cm ( : ρ ) 4 [ C], 1 [ ], 1.00 [g/cm 3 ].,.. [g/cm 3 ] , [m]. a 10 n ( 1 a < 10, n ) [km].

35 ( ), ( )., %. P ( :, ) [kg], [kg].,. P ( :,,,. )

36 27 3,,,,,,,..,.,,,, ,, 2, 3, 4.,,,, 179 [mm] [mm].,,.,.,,..,.,., ,., 1., (L) 10

37 [mm] ( ), [mm],, [mm] L < [mm]., 1 [mm],., [mm].,, 0 ( ), 0,., [mm], 4., [mm], 5., 4 5,., 1 (d) 3 3, ,. 3 1

38 (30 [m] ) [m] 1 [cm] [cm] [mm] 1 [mm] [mm] 10 1 (1 ) [mm] 1 [mm] [mm] 20 ( ) 1 (1 ) [mm] 100 [mm] 1 [mm] 1000 (1), [cm] (2),,, 0.1 [mm],, 0.1 [mm].,,. 10, 0.1 [g] 4.5 [g] 0.01 [g] 4.52 [g] [g] [g] 2, 3, 5., [g].. (1). : [g], [m] 5 ( 2, 0,.) (2) 0. : [m] (17.9 [mm] ) 2.15 [mv] ( [V] ) 3 ([mm] 17.9 [mm] [m], )

39 30 3 (3) 0 0. : 1.01 [g], 101 [m] 3 ( 0,. ) 1.01 [g] [mg], 1010 [mg]., 0., [mg], (1) 0.6 (2) 8.7 (3) 3.07 (4) (5) (6) (7) (8) ,., , ,, 45 2, , 24.65, 4., n , 3,, 5., , 5,, 7. n, (n+1). (1) (n+1), n : (2) (n+1), n : n

40 JIS JIS (Japanese Industrial Standard),, (1), (2). (3) (n+1), n 1 1/2, (i), (ii). (i) n. : (ii) n. : ,,,.,, , 1.,., ( ).,.,. (1) ( ),,. (2). (3),,.

41 , A, B, C 3. A [g], B 3.01 [g], C [g]. g.. (1) B 2, 3. A ( 4 ) B C (2) (3) 5.57 [g] ( 3 ) 2. A B ,. A 10 2, 4.41 [g]. B 10 3, [g] , A 2, B 3, = [g]., (, A 2 ), [g]. 2.. (1) [kg] [g] (2) [m] [m] [m] (3) [m] [cm] [cm] (1) 2,, 1.,.,.

42 ( 2 ) ( 3 ) (..) 4., [m], 5.11 [m] = [m 2 ] ( = [m 2 ] ), (5.11) 4 (10.17), 3. (2),. 5, , [cm] 3 [cm] = 375, 375 [cm]. (3), 1. 1, [m] S. π = , (3 ) 1., π = , π = S = π r 2 = (10.2) 2 = S = 327 [m 2 ].

43 (1),,,, 2.00 [m], 1.00 [m], 5.2 [mm]. V [m 3 ]. (2) [cm] V [cm 3 ]. π = , [m] 11 [m] 1111 [m] + 11 [m] = 1122 [m] = [m] [m] 1110 [m] 11 [m] = [m 2 ] [m 2 ] [m 2 ] (1). (2). (3). (4). 7., 0.50 [m], 2.08 [m] 1.05 [m]. π = (1) (1.05) = ( 3, π 4 )

44 (2) ( ) ( 2, 3 ) (3) = 4.46 (4) ( ) [m 2 ] 4. (1), [m], 2.02 [m] 0.50 [m]. π = (2), 20.0 [cm], [cm] 1 56 [cm 2 ] 10. (3), [cm], [cm] [cm]. π = ,.,. (,. ) 3, 3., ,,. (CD),.. CD, 0.1 [µm],

45 [mm] , 0.04 [µm].,,.,.,,,.,,,, , 0.5, 1.0, 1.5, 2.5. (,,. ),, 0.5, ( ) ±0.5 % (, 10 [ma], ±50 [µa] ), 3.,, ( ), 4., 1, [g].,, 2., [ml]., [mm].,, [cm].,.

46 (1) (2) (3) (4) (5) D [m]. m., π = [Ω] (R), (I), 10.1 [ma]. (V ) (P )., V = R I, P = R I 2. P [W] ( ). 600 [W], 400 [W] [A], 1 ( ) (Q), 1 [C] ( )., 1 N., [C], [C],. Q = I t., Q [C] = I [A] t [ s ] ([ s ] : )., Q = N e ( = 1 ) [ C] [g/cm 3 ] [L]., 1 [L] = 1000 [cm 3 ].

47 [m],, , tan = ,, [m].,,.,, ( [ ] ), ( [ ] ).

48 ,,,.., l = 2 π r, v = V sin(ω t + θ).. ( ),., ( ).,.,. 4.2,, 4 1.

49 (, ) A * α alpha, B * β beta, Γ * γ gamma, * δ delta, E ε epsilon, Z ζ zeta, H η eta,, Θ * θ theta,, I ι iota, K κ kappa, Λ λ lamda, M * µ mu, N ν nu, Ξ ξ xei, xi,, O o omikron, Π * π pei, pi, P ρ rho, Σ σ sigma, T τ tau, Υ υ y(u)psilon, Φ φ phei, phi, X χ khei, chi, Ψ ψ psei, psi, * Ω * ω omega,. 1. (1) 3. (2)..

50 ,,. TABEPNA. P [ ].. ( ). 4.3,.,,,,.,,,.., (unit)., 1, 4 4, ,,. 4.4,. 1, 1, 1., (kilo) (mili).,,. 4 2.

51 E P T G M * k * h da ( ) d c m * µ * n p f a *.,. }{{} (k) }{{}}{{} (h) (da) }{{} (m) }{{} (d) }{{}}{{}.. (c) (m),,. Ω,,. µ.. 4 2, k, m, c.

52 [m],,,.,., k ( ), m ( )., [km] [mm] [m] = [km] 1457 [m] = [mm], a 10 n (, 1 a < 10, n ), k ( ) = 1000 = 10 3, m ( ) = = 10 3, 1457 [m] = [m] 1457 [m] = [mm] = [mm]. a 10 n (, 1 a < 10, n ),,, 10 n,. 2., (. ), (1) 1230 [m] ( ) (2) 450 [mm] ( ) (3) 1.2 [kv] ( ) (4) [A] ( ) (5) 0.56 [MΩ] ( ) 3., (. (1) 2.94 [km] ( [m] ) (2) 38.4 [µm] ( [m] ) (3) 457 [kg] ( [g] ) (4) 9.86 [µω] ( [Ω] ) (5) 6.31 [MΩ] ( [Ω] ) ) 4.,. (1) [Ω] (2) [g] (3) [m] (4) [A] (5) [V]

53 I II III IV V VI VII VIII IX X, ,,,..,.,. 4.5 SI ( ) 4.5.1,,,,,,.,, 4 1,. 4 1

54 4.5. SI ( ) 45, (Système International d Unités [ ], SI ),., 1 [m], [kg], [ s ( )] MKS, 2 [cm], [ g ], [ s ] CGS, 3, MKS [A] MKSA, 4 [kgw] ( ). MKS,., [kgw].,, SI ( ) SI ( ) SI, [J], [Pa]., SI [kgw] [N] [kgw m] [cal], [kcal] [J] [mmhg], [atm], [kgw/cm 2 ], [N/m 2 ] [Pa].,. SI, 7 ( 4 3) 2 ( 4 4), ( 4 5), 10 (P )., SI,.,.

55 SI m kg s A K mol cd 4 4 SI rad sr 4 5 SI m 2 m 3 m/s m/s 2 kg/m 3 rad/s Hz,, J, N m V

56 ,,,. 3 [km] [m] [m], 15 [cm 2 ] [mm 2 ] [mm 2 ], 1.,,.,, [ g/cm 3 ( )], 1 [cm 3 ] 1 [ g ],. ρ [ g/cm 3 ] = m [ g ] V [cm 3 ] ( ). 1 [kg/m 3 ] ( g/cm 3 ), 1 [kg] = 1000 [ g ] = 10 3 [ g ] 1 [m] = 100 [cm] = 10 2 [cm] 1 [m 3 ] = 10 6 [cm 3 ], 1 [kg/m 3 ] = 103 [ g ] 10 6 [cm 3 ] = [ g/cm3 ] = [ g/cm 3 ]

57 ( ). (1) 20.8 [ g/cm 3 ] (kg/m 3 ) (2) [kg/m 3 ] ( g/cm 3 ) 2. d 10 [mm], h 100 [mm]. m. π = 3.14, S S = π ( ) d 2 2 = 3.14 ( ) = [cm 2 ], V, V = S h V = [cm 2 ] 10 [cm] = 7.85 [cm 3 ] 4 6 ρ 2.69[ g/cm 3 ], m m = ρ V = 2.69 [ g/cm 3 ] 7.85 [cm 3 ] = 21.1 [ g ] [ g/cm 3 ] , 1.83 [ g/cm 3 ]. 500 [ g ] [cm 3 ].

58 , ( v )., [m/s ( ) ]., 1 [m/s ( ) ] 1 [m/s] = 1 [ s ( )] 1 [m].., 1 1, 1 [m/min( )] = 1 [min( )] 1 [m] ( ) 1 [km/h( )] = 1 [ h ( )] 1 [km] ( ) [km/h]. [m/s]. 1 [km] = 1000 [m] 1 [ h ( )] = 3600 [ s ( )], 100 [km/h] = [m/s] = 27.8 [m/s] 8. ( ). (1) 10 [m/s] (m/min) (2) 20 [m/s] (km/h) m 10., km.. ( a ),., t 1 [ s ( )] v 1 [m/s], t 2 [ s ( )] v 2 [m/s].

59 50 4, ,, a = = = v 2 v 1 [m/s] t 2 t 1 [s]., [m/s 2 ( )]., 1 [m/s 2 ] = 1 [ s ( )] 1 [m/s]., a > 0, a < [km/h], 80 [km/h], 5 [ s ].., 50 [km/h] = [m/s] = 13.9 [m/s] 80 [km/h] = [m/s] = 22.2 [m/s], a = [m/s] 5 [ s ] = 1.7 [m/s 2 ]

60 (1) 36 km, km.. (2) 70 km, [N]. 1 [kg] 1 [m/s 2 ]. =, 1 [N] = 1 [kg] 1 [m/s 2 ] = 1 [kg] 1 [m/s 2 ] = 1 [kg m/s 2 ]., [m/s]. a = 9.8 [m/s] 0 [m/s] 1 [ s ] = 9.8 [m/s 2 ], 9.8 [m/s 2 ]., 9.8 [m/s 2 ] = g., g.,., [m/s]. m [kg], m g [kg m/s 2 ]. 1 [N] = 1 [kg m/s 2 ], m g [N].

61 [ g ],, [N]., 9.8 [m/s 2 ]. m = 800 [ g ] = 0.8 [kg] F = m g = 0.8 [kg] 9.8 [m/s 2 ] = 7.84 [kg m/s 2 ] = 7.84 [N] 11. ρ = 2.5 [g/cm 3 ], 8000 [cm 3 ]., 20 [km/h] 92 [km/h] 5 [ s ].,. (1) m. (2) a. (3) F = m a (, F :, m :, a : ),. 12., 49 [N], [m/s 2 ] ( P ), [Pa]. SI 1 [Pa] = 1 [N/m 2 ] ( 1 [m 2 ] 1 [N] ) [N], 0.5 [m 2 ]. [Pa]. 490 [N] 0.5 [m 2 ] = 980 [N/m 2 ] = 980 [Pa] 13. (1) 1 [N/cm 2 ] [N/m 2 ]. (2) 588 [Pa] [kn/m 2 ]. (3) 3500 [N/m 2 ] [kn/m 2 ].

62 [Pa]., 9200 [kg], 9.8 [m/s 2 ]., 2. 1, 1., 2,.,,.,., F [N], s [m],,,, W. W = F s. [J], [N m].

63 [J ( )], 1 [N], 1 [m]. 1 [J] = 1 [N m] [N] 40 [m] [J]. W [J] W [J] = 120 [N] 40 [m] = 4800 [N m] = 4800 [J] 15., 200 [kg] 10 [m]. [J]., 9.8 [m/s 2 ]. 16. ( ). (1) 300 [J] (N m) (2) 9800 [N m] (kj),.,.. W, t, P, P = W [J] t [ s ], [J/s]., [J/s],, [W( )] ( 1 [W] = 1 [J/s] )., [J ( )] [W h ( )], [W s ( )]., [W h] [W s].

64 , 1 [J] = 1 [N m] 1 [W] = 1 [J/s] 1 [W s] = 1 [J] 1 [W h] = 1 [W] 3600 [ s ] = 1 [J/s] 3600 [ s ] = 3600 [J]. 8., 2000 [kg] 1 25 [m]. [kw]., 9.8 [m/s 2 ]. 1 [kw] = 1000 [W] [kg] 9.8 [m/s 2 ] = [kg m/s 2 ] = 19600[N] [N] 25 [m] = [N m] = [J], P P = [J] 60 [ s ] = [J/s] = [W], P [kw] P = [kw] = 8.17 [kw] [N] 15 [ s ] 40 [m] [kg], 50 [ s ] 40 [m]. [kw]., 9.8 [m/s 2 ].

65 [W], 1 [ s ] [J]. 20. ( ). (1) 8.5 [W h] (W s) (2) 20 [W h] (J),.,., SI,, SI [cal], [mmhg], [atm]., 760 [mm], 1,. 1 [atm ( )] = 760 [mmhg ( )] = [Pa],, SI [kgw].,,., g = 9.8 [m/s 2 ]. ( )., ( W ), [kg], SI [N], SI [kgw]., [kgw], ( ) [kg].

66 ,. 1 [N] 1 [kg] 1 [m/s 2 ]., 1 [N] = 1 [kg] 1 [m/s 2 ] = 1 [kg m/s 2 ], 1 [kgw] 1 [kg] g = 9.8 [m/s 2 ], 1 [kgw] = 1 [kg] 9.8 [m/s 2 ] = 9.8 [kg m/s 2 ]., [N] [kgw] 1 [kgw] = 9.8 [kg m/s 2 ] = 9.8 [N] 1 [N] = 1 [kgw] 9.8 = [kgw]

67 (1) 0.5 [kgw] [N]. (2) 0.7 [kn] [kgw]. (3) 800 [g], [gw].,.,, SI., [J] ( [kj], [MJ]). 1 [J( )] = 1 [N] 1 [m],,.

68 , (J.P.Joule),,,. 1 [cal] = 4.2 [J] 1 [J] = 0.24 [cal].., 1 [cal] = 4.2 [J]., 1 [kcal] = 10 3 [cal] = [J] = 4.2 [kj] 1200 [N], 5 [m], [kcal]. W = 1200 [N] 5 [m] = 6000 [N m] = 6000 [J] = 6 [kj] 1 [kcal] = 4.2 [kj] 6 [kj] = [kcal] = 1.4 [kcal]. ( ). (1) [cal] (J) (2) [J] (kcal) (3) 0.4 [kcal] (J)

69 [m/s]. [km]. 2., [km] [km/h]. 3., 40 [km/h] 4 [ s ]. [m/s 2 ] [m], 2.00 [m], 2.00 [mm].., [N]., 7.86 [g/cm 3 ] [cm], 20 [cm] 2 [ t ], [kpa]., 9.8 [m/s 2 ] [m], 10 [m 3 ]., [kw]., 1000 [kg/m 3 ], 9.8 [m/s 2 ] [kg] 5 12 [m/s].

70 61 5,,,.,,,,,,,. ( ),,,.,,. 5.1 C = 90 ABC, BC = a, CA = b, AB = c. a, b, c, b a, a b, c b, b c, a c, c a 6., 3., A = α, B = β. (, α + β = 90. ) a = sin α (, ) c sin, sine. b c a b α sin ( ). a = 3.0 [m], c = 5.0 [m], sin α = 3.0 = = cos α (, ) cos, cosine. = tan α (, ) tan, tangent., a = 3.0 [m], b = 4.0 [m], tan α = 3.0 =

71 62 5, sin, cos, tan,. sin, cos, tan.., (,.),,., α,, β ( ). (, β, C,.) sin β = b c cos β = a c tan β = b a, sin, tan.. (1) sin, s. AB BC. sin α = BC AB (2) cos c,., AC. cos α = AC AB (3) tan t., tan α = BC AC

72 , 2., 2,,. 2., I, II. I, A = B = 45, C = 90. CA = BC = a,, AB = 2 a,, CA : BC : AB, 1 : 1 : 2, sin 45 = a = 1 2 = 2a 2 2 cos 45 = a = 1 2 = 2a 2 2. tan 45 = a a = 1, II, A = 30, B = 60, C = b, AB = 2 b, BC = b, AC, AC 2 + BC 2 = AB 2,, AC 2 = AB 2 BC 2 AC = AB 2 BC 2 = (2 b) 2 b 2 = 3 b 2 = 3 b, 3 AB : BC : CA, 2 : 1 : 3., sin 30 = b 2 b = b 3 cos 30 = = 2 b 2 tan 30 = b = 1 3 = 3 b 3 3

73 64 5, 3 b 3 sin 60 = = 2 b 2 cos 60 = b 2 b = b tan 60 = = 3 b.,, ( )., sin, cos, tan 3., ( ),.. A = θ ( ). α, β, θ. c a = cosec θ. cosecant ( ) c b = sec θ. secant ( ) b a = cot θ. cotangent ( ) 4.1, cosecθ = 1 sin θ, sec θ = 1 cos θ, cot θ = 1 tan θ. 6. sin, cos, tan.

74 5.3. sin cos sin cos, sin, cos, tan., sin α = a c, cos β = a c, sin α = cos β, α + β = 90, sin α = cos(90 α).,. sin β = cos(90 β) cos α = sin(90 α) cos β = sin(90 β), sin 15 = cos 75, cos 50 = sin 40. tan, tan α = a b, tan β = b a 1 tan β = tan α = 1 tan(90 β)., 0 < α < 90, 0 < β < 90., α, β,., tan α = a b,. a c = sin α, b c a b = a c b c = cos α tan α = sin α cos α., α (, tan 90 ).

75 , 90, α β, 0, 90,., ( ) 0, 90,. (,.),. α 0, β 90 ( α 0, β 90 ). b c, a 0. sin α = a c, α 0, a c. a, c 0., sin 0 = 0., cos α = b c, cos 0 = 1., β 90 b c. b c 1. sin 90 = 1., a 0 a, c 0., cos 90 = 0., tan 0, tan 90. tan α = a b, α 0, a, 0 a., b 0 tan 0 = 0. tan β = b a, β 90, a b, tan β.,, 0, 30, 45, 60, 90.

76 5.4. 0, θ sin θ cos θ tan θ , θ, (.)., θ,., θ, c, a, b a c = sin θ a = c sin θ b c = cos θ b = c cos θ , sin θ, cos θ, sin α, cos α, tan α, sin β, cos β. 2. a, b.

77 ,., a 2 c 2 a 2 + b 2 = c 2. c 2, + b2 c 2 = 1, sin θ = a c, cos θ = b c a 2 ( a c 2 = c b2 c 2 ) 2 = (sin θ) 2 = (cos θ) 2, (sin θ) 2 + (cos θ) 2 = a2 c 2 + b2 c 2 = a2 + b 2 c 2 = c2 c 2 = 1., (sin θ) 2 = sin 2 θ, (cos θ) 2 = cos 2 θ, sin 2 θ + cos 2 θ = 1.,,., θ. 3. sin 2 θ + cos 2 θ = 1 θ = 0, 30, 45, 90. ( 5.4.) sin α = a c, cos α = b c, tan α = a b, tan α = sin α cos α cos(90 α) = a c = sin α sin(90 α) = b c = cos α tan(90 α) = b a = 1 tan α sin 2 θ + cos 2 θ = 1 a = c sin α, b = c cos α, a = b tan α

78 , , 0 90., (, ), sin θ, cos θ, tan θ, θ,, θ.,. y = x 2 y x 2.,, sin 15, cos 15., θ = 15,, a, b, c, a c, b c sin 15, cos 15.,.,.. 1 sin, cos, tan 0 90., sin θ, cos θ, tan θ.,. sin 15 = , cos 15 = , tan 15 = (1) tan 38 (2) cos 60 (3) sin 75 (4) tan 53 (5) cos 8 5. θ. (1) sin θ = (2) cos θ = (3) tan θ = 2.36, 0 90., ,,

79 70 5., 0 90,. 6.. (1) sin 43, cos 25, tan 86. (2) sin cos 2 37 = 1. (3) cos 40 sin 50 sin 70 cos [m] A B, 55 (.). 1.5 [m]., C 1.5 [m] D. ABD, BD = tan 55 AD, tan 55,, BD = AD tan 55 = = 22.8 [m] BC = BD + DC = = 24.3 [m]

80 [m] AB A, C, 30. BC x. 2.. (1) B AC D. BD. (2) S [m 2 ]. (3) BC. 3., A = 90, AB > AC ABC, AD BC, BC = 13, AD = 6. (1) BD, CD. (2) cos θ.

81 ,. XX, YY A B. A X, C B BCA = 39. C, X 30.0 [m] D B BDA = 27. AB m (, AB = a, AC = b )., tan 27 = 0.51, tan 39 = A C α., A a [m] B β. h. ( : BD = b. α, β, b, h. )

82 ,,.,..,,,. 6 2,,.,..,,,. 6 3

83 74 6, ( ) ,.,. 6 6, 3 [kg], 1 [kg] 3., 3. 1 [kgw], 1 [kg].,,,. 6 6,,.,,. 6 7, a, a., a, a = a. 6 7 a a,,.,,,, a.,,.

84 a = b 2 a b, 1, 2,. 6 8, a 1, 2, a n. d = n a, d a n., n = 2 d = 2 a, n = 3 d = 3 a. 6 9, a, 2 a a 2, 3 a a a n, (scalar).,,,,,,.,.

85 a, b, c, a + b = c, c a b a + b = c a b,. a b,., 6 10 a = OA., a A b. b B, O, B OB c. 2., a b 2. 2, 6 10., O OB a + b = c.

86 a b.,. ( a b = a + ) b, a b. a b, 6 11., ( a b = a + ) b = d a b = d , d + b = a, a b = d a = OA, a = AB. a a = a + ( a ) = OA + AB (, ), B O. OB,, 0,.,. a a = 0 0, 0.

87 a, b.,. (1) a + b (2) 2 a (3) 2 b 2. 1 a, b, (,, ). (1) a b (2) a + 2 b (3) 2 a 3 b 2. ABC, AB + BC + CA. AB + BC = AC AB + BC + CA = AC + CA = AC + ( AC) = 0

88 ABC. (1) BC + CA (2) AB AC (3) AC BC 6.6.,,,. (1) a + b = b + a (2) ( a + b ) + c = a + ( b + c ), m, n (3) (m + n) a = m a + n a (4) m ( a + b ) = m a + m b. 4.. (1) 2 (3 a ) (2) 2 a + 3 a (3) 4 b b (4) 3 ( a + b ) 2 ( a 2 b )

89 a, b, 1 c ( = a + b ).., 1 a, 2 a 1, a 2,. a = OP, a 2 OA, OB. P OB, OA, OA, OB P 1, P 2. OP 1 = a 1, OP 2 = a 2, a = a1 + a 2., a OA, OB 2 a 1, a 2. OA, OB, OA, OB, OA x, OB y. 6.8, x, y O a = OP, x, y. x a 1 = OP 1, y a 2 = OP 2. P 1, P 2, P (a 1, 0), (0, a 2 ), (a 1, a 2 ), a a a = a a 2 2., a 1 a x, a 2 a y. 6 12, 1, x, y, x i, y j. i e 1, j e 2.

90 i, j,, a1 = a 1 i, a2 = a 2 j a = a1 i + a2 j.,, a = (a1, a 2 ) 6 13., i = (1, 0), j = (0, 1)., a 2. a = a1 i + a2 j = ( a1, a 2 ),,. (1) (a 1, a 2 ) = (b 1, b 2 ) a 1 = b 1, a 2 = b 2, a = b, x, y. 2. (2) (a 1, a 2 ) + (b 1, b 2 ) = (a 1 + b 1, a 2 + b 2 ) a, b a + b, x, y , k, (3) k (a 1, a 2 ) = (k a 1, k a 2 ), m, n, 6 14 (a 1, a 2 ) + (b 1, b 2 ) (4) m (a 1, a 2 ) + n (b 1, b 2 ) = (m a 1 + n b 1, m a 2 + n b 2 ) (3), (4).

91 a, b, c, d, e, a, b, c, d, e. ( ),. a = ( 3, 2 ), a = = 13 b = ( 2, 3 ), b = = 13 c = ( 4, 2 ), c = ( 4) 2 + ( 2) 2 = 2 5 d = ( 3, 2 ), d = ( 3) = 13 e = ( 0, 4 ), e = ( 4) 2 = 4 4. a = (3, 2), b = (2, 3), a + b,. a + b = (3 + 2, 2 + 3) = (5, 5) a + b = = 50 = a = (3, 2), b = ( 2, 1),,. (1) a + b (2) 3 b (3) 2 a 3 b (4) a + 2 b

92 x, y 2 A, B, AB AB. AB = (b 1 a 1, b 2 a 2 ) AB = (b 1 a 1 ) 2 + (b 2 a 2 ) x, y 2 A, B, AB AB. AB = (4 1, 3 2) = (3, 1) AB = = x, y 2 A, B, AB, AB. (1) A (4, 2), B ( 1, 5) (2) A (6, 3), B (1, 4) (3) A (0, 5), B (2, 1) 7. O 2 F 1, F 2 ( 1 1 [N] ). (1) F 1, F 2. (2) F 1, F 2 F. (3) F. (4) F F.

93 a = OP x θ. a = a, 6 17 a 1 a = cos θ, a 2 a = sin θ, a a 1 = a cos θ, a 2 = a sin θ,, 6 17 a a = a1 + a 2 = a 1 i + a2 j = a cos θ i + a sin θ j = (a cos θ, a sin θ). x, y,. 7. a = 10, θ = 60, a = (a 1, a 2 ) a 1, a 2. a = (a 1, a 2 ) = ( 10 cos 60, 10 sin 60 ) ( = 10 1 ) 3 2, 10 2 = (5, 5 3) a 1 = 5, a 2 = a = 5, θ = 30, a = (a 1, a 2 ) a 1, a 2.

94 ,,.,, F 0,,., 6 18, O 3 F 1, F 2, F 3,,. F 1 + F 2 + F 3 = OA θ, OB., W [N] P, B, P., P S, N., P, W, S, N., x, y (x, y. OA x ).

95 86 6, x, y, S, N x, y,., W,. W = (W x, W y ) = ( W sin θ, W cos θ ) P, 0, x S W sin θ = 0 y N W cos θ = 0 S = W sin θ [N], N = W cos θ [N] 9., P W 10 [N], θ 30, S N, [N]. S = 10 sin 30 = = 5.0 [N] N = 10 cos 30 = = 8.7 [N] 9. W = 50 [N]. θ = 45, 0., S [N], N [N].,. (1) N, S, W, θ,. (2) N, S, W, θ,. (3) S [N] N [N]. ( )

96 [N] P, O 2 OA, OB,. OA, OB S 1, S 2, P W ( 20 [N]),. (1) x, y, S 1, S 2 x, y. (2) x, y 0 ( ) (, W ). (3) W, S 1, S 2 (, 2 = 1.4, 3 = 1.7 ). 6.11,., ( ). v ( V ) , 6 19 A v A. B v B., C B, B., B

97 88 6 C A A B v A v B C B v A + v B C B (C B) v, v = va + v B., OA, OB 45,., OA P 30 [km/h] v P, OB Q 60 [km/h] v Q., Q P v Q P v Q v P P Q v Q v P,, P Q (P Q). 6 21

98 , v P = 30 [km/h], v Q = 60 [km/h], OA x, y OA, v P, v P = 30 i = (30, 0), v Q, 6 22 v Q = 60 cos 45 i + 60 sin 45 j = 30 2 i j = (30 2, 30 2 ), 6 22 v Q v = (vx, v y ) = v Q v P,., v, 6 23 α. tan α = v y v x = = 3.43, α. α 74 = ( , ) = (12.3, 42.3) v = v = = 44.1 [km/h] 6 23 v, P Q 74, 44.1 [km/h].

99 V 1 = 0.5 [m/s], V 2 = 0.3 [m/s] 50 [m].,.,, [m], 6.0 [m/s]. A B, 8.0 [m/s]..,.,.,.,,,.,.,,,.,.,.

100 ABC,. (1) AB AC CB. (2). BC BA ( a 4 b + c ) 2 ( a 2 b + c ) 3.. F 1 = (2, 2), F 2 = (2, 2), F 3 = ( 3, 4) (1) F. (2) F. ( ) (3) i, j F. (4) F x ( ) [N] P, A 20 [cm], 30., S 1, S 2, P W,. (1) x, y 0 ( ). ( W ) (2) S 1, S 2. ( ) (3) P. h.

101 , 30, 10 [N] 45.,. (1) S, N, W,.,. (2) x y,. (3) (1), (2), S, N. 6. A 36 [km/h]., 100 [m] B 54 [km/h]. A B,. 1 [m/s] = 3.6 [km/h]

102 93 7, ph ( ) 4 5. ph (mol/l), ph = 10 5 (mol/l).,.,,.,,.,,.,,.,.,, NTC.,., 7 1,,.,., ,.,,

103 94 7,,,.,, a, N a m = N ( ) m. m, a ( ) N (Logarithm; ) m = log a N ( )., N, a m (log a N, a, N ). a m = N m = log a N ( ) ( ),,, = 16 4 = log = = log , a 0 = 1 0 = log a 1,. a 1 = a 1 = log a a (1) log a 1 = 0, log a a = (1) 2 3 = 8 (2) 5 2 = 25 (3) 3 4 = 81 (4) = 1.41 (5) = 4

104 a N. (1) log a 16 = 4 a 4 = 16 a = 2 (2) log 4 N = = N N = 4 = 2 2. a N. (1) log 9 N = 2 (2) log a 125 = 3 (3) log a 27 = 3 (4) log 49 N = 1 2 (2) a 1, A, B log a AB = log a A + log a B log a A B = log a A log a B 1 log a A n = n log a A 2 log a n A = 1 n log a A n A = A 1 n. P , 100 = = 10, A = A 2. [ log a AB = log a A + log a B 1 ] log a A = m, log a B = n A = a m, B = a n AB = a m a n = a m+n m + n = log a AB log a A + log a B = log a AB ( )

105 96 7 [ log a A n = n log a A 2 ] n log a A n = log a A } A {{ A A} n = log a A + log a A } A {{ A} n 1 ( 1 ) = log a A + log a A + log a A } {{ A} n 2 = = log a A + log a A + log a A + + log a A }{{ A} 2 = log a A + log a A + log a A + + log a A + log a A }{{} n = n log a A ( ) 2, log a A n, n log. 2, n. 3. 1, log a A B = log a A log a B. 4. 2, log a n A = 1 n log a A. 5. log a 2 = x, log a 3 = y, x, y. (1) log a 6 (2) log a 3 2 (3) log a 1 2 (5) log a 3 2 (6) log a 6 (7) loga 8a 2 (4) log a 9 8 (3) a, b 1, A log a A = log b A log b a

106 log a A = c., a c = A. a c = A b log b a c = log b A c log b a = log b A log a A log b a = log b A log b a 0. log a A = log b A log b a 6. log b a log a b = ,., N, 10, log 10 N = log N., N log N., log 10 1 = 0, log = 1 log 1 log 10 log 1 = 0, log 10 = 1, 1 10 (N) (m), 0 1.

107 a m = N m = log a N ( ) ( ) a = 10 ( 10 ), 10 m = N m = log N ( m :, N : )., 10 m = 2.00 m = log 2.00,, , = = log (N) (m) 10 m = N m = log N ( ) (N) 1.00 N < 10.00, ( ) (m) m < log 3 = , 30, 300, log 3 = log 30. log 30 = log( 3 10 ) = log 3 + log 10 = = ( log A B = log A + log B ) 4. log 3 = log 0.3. log 0.3 = log( ) = log 3 + log 10 1 = ( 1) =

108 , log 2 = 0.30, log 3 = 0.48, log 7 = (1) log 9 3 (2) log 5 14 (3) log 2 9 log log 2 = , log 3 = (1) log 200 (2) log (3) log 6 (4) log 5 log ln log, 10, e (2.718 ), log e ln.., e. e , t [ C], R [kω] R = b 10 at ( a, b,, 7 2.., R = b 10 at ( log ). log R = log ( b 10 at ),,, log R = log b + log 10 at log R = log b + a t log 10 log R = log b + a t y = a x + b., log,. 9., (. ) 1 at (1) 5 y = 2 x (2) N = b 2

109 ,,.,, f., 3...,. (1). (2) log,. (3).

110 f [Hz] log f f [Hz] log f f [Hz] log f ,,.

111 ,.,,. ( Hipparchus ; BC 120 ), 1, 6,. ( N. P. Pogson ; ), ,.,,.... y = a x x = log a y 2 4 = 16 4 = log 2 16,., = 10 6, 10 ( ), log = 6,

112 ,., = 10 6 ( 10 ), log = 6, , 10, = k log , k., 10 1, log log 1 = = k ( 4) k = 2.5,. m, F, F 0 1, m 1 = 2.5 log F F 0., ( ), ( ),, UFO. 4, 1., 1.

113 104 7, 4, 1,., 4 1 = 2.5 log F F 0 5 = 2.5 log F F 0 log F F 0 = = 2 1,, F F 0., log F F 0 = 2 F F 0 = 10 2 ( log X = a X = 10 a ) ,,., 2.,., 2.., F 1 2 = D 2 F 2 = 2 D 1 =., ( D2 D 1 ( D1 D 2 ) 2 ) 2 m 1 1 = 2.5 log F 1 F 0 m 2 1 = 2.5 log F 2 F 0 ( m 1 m 2 = 2.5 log F 1 log F 2 F 0 F 0 )

114 log x y = log x log y m 1 m 2 = 2.5 { ( log F 1 log F 0 ) ( log F 2 log F 0 ) } = 2.5 ( log F 1 log F 2 ) = 2.5 log F 1 F 2. F ( 1 D1 = F 2 D 2 ( D1 m 1 m 2 = 2.5 log D 2 ) 2 ) 2. log X n = n log X., m 1 m 2 = 2.5 ( 2) log D 1 D 2 = 5 log D 1 D 2.,.., [pc] ( parsec : ) 26.7., 10 [pc],. (, [m],, [pc].), log 4.85 = m 1 = 26.7 [ ], D 1 = [pc], D 2 = 10 [pc] m 2 m 1 m 2 = 5 log D 1 D 2 m 2 = m 1 5 log D 1 D 2.

115 106 7, m 2 = log( ) = ( log ) = ( ) = 4.9 [ ].?? 10 [pc]. 1,!, 1 [pc] = [m]. ( P ) 10., 10, ph ( ;, (ph) ; ), ph, power of Hydrogen ( ) 8.3, , ph, 3.3 ph, 7.4., ph. 12.6,, [H + ] ( [ ] ). (mol/l). ph

116 [H + ], 10 1 (mol/l) (mol/l).,. ph,,. ph, ph = log 1 [H + ] = log 1 log[h + ] = 0 log[h + ] = log[h + ]. ph ph = log[h + ], [ ]. 2.0 [m], 5.0 [kg], ph, [H + ], (mol/l).,. ph = 1.0 ph = 1.0 = log[h + ] log[h + ] = 1.0 = ( 1) 1.0 = ( 1) log 10 = log 10 1 log [H + ] = 10 1 (mol/l)., ph = 2.0 [H + ] = 10 2 (mol/l),.,.

117 108 7 ph [H + ]( ) = 10 6 (mol/l) ph. ph, ph = log[h + ], ph = log 10 6 = ( 6) log 10 = ph = 2.5., = 3.2. ph, ph = log[h + ], 2.5 = log[h + ] log[h + ] = 2.5 log X = a X = 10 a [H + ] = = = = (mol/l).

118 ph., log 2 = 0.30, log 3 = 0.48, log 7 = (1) (mol/l) (2) (mol/l) (3) (mol/l) 12. ph., = 3.2. (1) ph = 5.0 (2) ph = ( ),.,,.,,,. ( SPL : Sound Pressure Level ). (decibel) [db], = 20 log [db].,,, 1000 [Hz] ( ) ( [ ], P 0.). ; P 0 = [N/m 2 ] = [Pa]. (N. Pa.),,,,,., ( ) P. P 0 P P, ( P 0 ).,, P = 0.1 [Pa], P = 100 [Pa].

119 110 7 P 0 = [Pa], P = 100 [Pa],. 20 log P P 0 = 20 log = 20 log = 20 ( 7 log 10 log 2 ) = 20 ( ) = 134 [db],,, P = P 0 = [Pa], 20 log P P 0 = 20 log = 20 log 1 = 0 [db]., 0 [db]. 0 [db] 134 [db], , , P = 0.10 [Pa]. [db]., log 2 = [db].., = 3.2, log 2 = 0.30., [db],, [db], 100 [db].,, ( ), 100 %,.,..

120 ,, [Pa], 60 [Pa] 10 6,,, 16 [Hz] 16 [khz] 10 3.,. 1 [khz] [Pa]. 1, 0 [db] (,, ) 10, 60 [Pa] 130 [db]. 1 [khz] [db] [phon ( ) ],.,, 1 [khz], [phon]..,,. 80 [db].,.., 80 [db], 0.2 [Pa].,. x 80 [db] = 20 log [Pa] = 20 { log x log( ) } log x = 4 + log( ) = log( ) x = 0.2 [Pa]

121 112 7.,,.,,.., [db], 20 log P, P 0.,,,., ph,., K K = (1/t) ( log C 0 log C ). C 0, C t.,,.

122 , log 2 = 0.30, log 3 = 0.48, log 7 = (1) log 35 (2) log 600 (3) log 0.9 (4) log 2 9 (5) log 6 7 (6) log , 20%, 1%,., 5%, log 2 = , , 10, 1, 100., log 2 = A A,., = , ph , ph = 5.1,. (mol/l)., = 7.9.

123 ( ), 1 80 %. 100 [db] 40 [db],. 7. ( ) G, 40 [db]. [V] 1 [V]., G [db], V o [V], V i [V]. G = 20 log V o V i

124 ,,., 1 360,.,.., θ = XOP, OX ( ), O OP ( ). OX OP,,.,,,., OP 50, 310., 90, 180., OP 1, = 410., OP,.. OP, = 310. OP θ, θ = α n ( n = 0, ±1, ±2, ). (n )

125 , α. ( 0 α < 360 ) (1) 480 (2) 150 (3) 740 (4) X OX, Y OY, XOY, YOX, X OY, Y OX 1, 2, 3, 4 ( x, y, )., θ = 45 1, θ = 150 2, θ = 100 3, θ = ( x, y ) (1) 380 (2) 250 (3) 235 (4) OP r, x, θ P ( x, y ). x, y,., sin θ = tan θ = y r y x, cos θ = x r, ( x 0 ) sin θ, cos θ,. 1 ( 0 < θ < 90 ), 2, 3.

126 , θ = 150. x < 0, y > 0 1 sin 150 = y r = 2 r = 1 r 2 = 0.5, sin 30 = 0.5., sin 150 = sin 30, 150 =180 30, θ, sin(180 θ ) = sin θ. 3 cos 150 = x r = 2 r 3 = r 2 3 cos 30 =, cos 150 = cos 30., θ, 2 cos(180 θ ) = cos θ. 3, θ = x < 0, y < 0 sin 210 = y 1 r = 2 r = 1 r 2 sin( ) = sin 30., 3 cos 210 = x r = 2 r 3 = r 2 cos 210 = cos( ) = cos tan ( ) sin θ, cos θ, tan θ.

127 θ y = sin θ, y = cos θ, y = tan θ. 1 ( ) sin θ, cos θ, tan θ. 2 4,. 1 y = sin θ ( 0 θ 360 ) θ, sin θ. θ sin θ θ sin θ y = sin θ, θ = α n,.,. 2 y = cos θ ( 0 θ 360 ),. θ cos θ 1.00 θ cos θ, sin θ 90.,.

128 cos θ y = tan θ ( 0 θ 360, 90, 270 ) tan θ, sin θ, cos θ.,. θ tan θ 0.00 θ tan θ 5. (1) 2 sin θ = 0.40, cos θ, tan θ. (2) 4 tan θ = 2.00, sin θ, cos θ. 6.,. (1) sin 115 (2) cos 223 (3) tan( 38 ) (4) cos 403 (5) sin( 412 ) (6) tan 949

129 , ( ). 30, 420, , (, )., ( ). r, r AB ( AB ), AB AOB= α., 2 π r, α 360 = AB 2 π r = r 2 π r = 1 2 π, α = π = π 3.14 ( ). α (radius) (angle), (radian). radian [rad]. 1 [rad], 57.3., 1 [rad] = 180 π, π [rad] = 180, 2 π [rad] = 360.,, [rad].,. sin sin, sin 30, 30 [rad] sin. 7. [rad]. (1) 30 (2) 45 (3) 60 (4) 90 (5) 270 (6) (1) sin π 6 (4) tan π 3 (2) cos π (3) sin π 4 2 (5) cos 5 π (6) tan ( 4 ) 3 π

130 ,,, (,, ).,,, 60, (,, [rad].).., 90?, ( ), (1 ) 360, 1, 1., 1 360, 1 4 (90 )., = 60, ( ), 1 = 60, ( ), 1 = 60, ,. 1. ; l AOB = 1 [rad], AOC = θ [rad], 1 r = θ l, l = r θ., l = 2 π r θ 2 π, l = r θ

131 122 8, 60 AOC = θ, l 2 π r = θ 360, l = π r θ 180, l,. 2. ; S AOB = θ [rad], S = π r 2 θ 2 π = 1 2 r2 θ, AOB= θ, S = π r 2 θ 360 = π r2 θ 360, [rad]. 2,,,, [rad].,. [rad] [rad].,, [rad]., [ : ω ( ) ], 1 (second) ( = 2π [rad] ), ω = 2 π 60 = π 30 [rad/s]. ( [ s ] second )., [rpm] revolution per minute ( 1 ). [rad/s]., 600 [rpm], [rad/s]

132 ,.,,.,?.,,,.,.,,,,.,.,,....

133 θ ( sin θ, cos θ, tan θ ),., [ ] [rad], [rad] [ ]. (1) θ = 24 (2) θ = 481 (3) θ = 4 3 π [rad] (4) θ = 13 ( π [rad] (5) θ = 3 7 ) π [rad] , θ, ( 0 θ < 360 ). 3 (1) θ 2 sin θ =, cos θ tan θ 2 (2) θ 4 cos θ = , sin θ tan θ 3. y = sin 2θ ( 0 θ 360 ). θ sin 2θ 0 θ sin 2θ θ sin 2θ

134 125 9,,.,, ( )., 1 2,, ,?,.,,. (1) ( ).,., ( ) ( ),. (2), 1,.,.

135 126 9 (3), ( ).,, , ,,, 1.00, 2.00, 3.00, 4.00, 5.00 [ma],. 1. [ma] [V]

136 ,.,,.,,.,,,.,.,,,,..,. (,,,.)

137 , 1. 1,. y = a x + b ( a 0, a, b ), y x 1, y x 1. a, b a = y x b y. (, x, y, x y.) 2 (x 1, y 1 ), (x 2, y 2 ). y 1 = a x 1 + b y 2 = a x 2 + b y 2 y 1 = a x 2 a x 1 = a (x 2 x 1 ) x 2 x 1 a = y 2 y 1 x 2 x 1 = y x 3 1, a, b, , (1), 1., 5.00 [ma] 5.50 [V]. (2), 9.1.3, a y b,. ( x I, y V ), y b 0., 2, (0, 0) A (4.50, 4.40), 3. a = y x = V I = 4.40 [V] 0 [V] 4.50 [ma] 0 [ma] = [Ω] = [kω] = 4.40 [V] [A] a, R

138 , V = R I ( R = [kω] ).,., R. V = R I R. [ma] [V] [kω] R 1 ( ) = 1.01 [kω] 5,., 5.00 [ma], 4.75 [V], [kω].,,.,,. (3), [ma], [ma],.,,., 9.78 [V] ,.., ( ).,,.,.,.,.

139 , x F,. F = k x, k,. 1. L = 30 [cm] 1 ( w [N] ), x [cm],., L 2 ( 2 L = 60 [cm] ) 2,. L w [N] x [cm] L w [N] x [cm] (1). (2) k, x w. (3) 1, 3.0 [N],. (4) 2,.

140 (1) L (2) (i) k = w x = (ii) k = w x = L = [N/m], F = 83 x = [N/m], F = 41 x (3) 3.0 [N] ( [N/m] ) = [m] = 3.6 [cm] (4) 2, 2. y = a x + b 1, w = 0 [N], y = 0 [cm], b = 0, y = a x. 1.,. w, l,. w [N] l [cm] (1). (2) k., l w. (3) 1.00 [N],.

141 ( ),., 1 [ C], 2., ( : α ) [cm],,. t [ C] l [cm] (1). (2) 25 [ C],.,,. (α) = [m] [K] [m] ( [1/K] ) (3) 20 [ C],. (4) 20 [ C] [m]. 10 [ C], 50 [ C] [cm].,, (2). (5). 100 [km], 60 [ C], [m].,,.

142 (1) (2) (α) = [m] [K] [m] ( [1/K] ). 20 [ C], 120 [ C] 2,, α = = [1/K]., [1/K]. (3) 20 [ C] t [ C] l, 20 [ C] l 0 l = l 0 { 1 + ( t 20) }. (4) 10 [ C] l 0 = 25 [m],, 50 ( 10) = 60 [ C]. l = 25 [ 1 + { 50 ( 10) } ] = [cm]. (5) l = ( ) = [m].

143 [cm]. t [ C] l [cm] (1). (2) 20 [ C],. (3) 20 [ C],. (4) 0 [ C] [cm]. 500 [ C]., (2).,.,.,.,. 9 1 Pt Au Ag Cu Al Fe Ni W ( 10 4 [1/K], 0 [ C] 100 [ C] ).

144 t [ C] ρ [µω cm] (1). (2). ( 1 [ C] ) (3). (4) 0 [ C] 500 [ C].. ρ = ρ 0 { 1 + ( t 20) k } k :. (,, ),.,,.,,.,., 82 : [ C] 100 [µω cm], ,,

145 ,. 2. y = a x 2 + b x + c ( a, b, c a 0 ) 2, y = a (x 2 + ba ) x + c { ( = a x + b ) } 2 b2 2 a 4 a 2 + c ( = a x + b ) 2 b2 4 a c 2 a 4 a. p = b 2 a, q = b2 4 a c 4 a, 2, y = a (x p) 2 + q 2. y = a x 2 x p, y q, y = a x 2 + b x + c y = a x 2 x p = b 2 a, y q = b2 4 a c 4 a.,, ( b ) 2 a, b2 4 a c 4 a., a > 0, a < [km] ( 40 [m] = 40 [m/s] ).. t [ s ] l [m] (1) l y, t x, y 2.

146 (2) y = a (x p) 2 + q, p q. (3) 6, 7, 8. (4) ( ),. (1) y, x, 2 y = a x 2 + b x + c. 0 x = 0, y = 0., c = 0, y = a x 2 + b x. 2, 4 x = 2 y = 60 = 4 a + 2 b 1 x = 4 y = 80 = 16 a + 4 b b 120 = 8 a + 4 b ) 80 = 16 a + 4 b 40 = 8 a a = 5 1 b = 40 y = 5 x x 3 (2) y = 5 x x = 5 (x 2 8 x) = 5 (x x) = 5 (x x ) = 5 { (x 4) 2 16 } = 5 (x 4) , 4, 80 [m]. (,.) (3) 3 x = 6, 7, 8, 60, 35, 0 [m].. t [ s ] l [m]

147 138 9 (4) [m] 4, x [m] y [m 2 ]. (1) 2. (2) y = a (x p) 2 + q, p q., x. (3) x 1, 2, 3, 4, 5, 6 [m]. (4), [cm] y [cm 2 ] x [cm]. (1) y, 2. (2) y = a (x p) 2 + q, p q., x. (3) x 2, 4, 6, 8, 10, 12, 14, 16, 18 [cm]. (4),.

148 ,..,.,..,,.,.,. [ 1 ] ( ).,,.,,.,.,,.. t [ C] R [Ω] ,,.,.,, log R, log R = a + b x. log R = y y = a + b x. 1, a y, b., log R = a + b x log R = 10 a+bx,. a, log 4600 = , x 1 = 0 y 1 = log 4600 = 3.66, x 2 = 100 y 2 = log 100 = 2., y x = y 2 y 1 x 2 x 1 = =

149 140 9, R = 10 ( x) = x = x. ( ) ( ),. [ 2 ] [ 1 ],,. y = a x b.,. (.),., y, x y = a x b.,, log y = log a + b log x. Y = log y, A = log a, X = log x Y = A + b X, 1. Y A = log a, b.

150 ,.., 5.,,.,,.,., (, ), (C) ( y ),. y = k C n ( k ), 5 (C), ( y ). (C).,. log y = log k + n log C, log y = Y, log k = a, log C = x Y = a + n x. 1,, n, Y a, k.,,.

151 ( L = 30 [cm] ) 2,,. (1) k. (2) 2, W [N] ,. L = 30 [cm] 2 W [N] x [cm] k, x W.,, 14.0 [N],.

152 ,,., force, f F. (Newton) [N],., v [m/s], /, /. [m/s]. ( ) α, β, γ, θ, [ ], [rad] angle l, L [m] length A, S [m 2 ] area, square V [m 3 ] volume t [s] time u, v, w, c [m/s] velocity a [m/s 2 ] acceleration ω [rad/s] angular velocity α [rad/s 2 ] angular acceleration, f, ν [Hz] frequency 143

153 λ [m] wave length m [kg] mass ρ [kg/m 3 ] density p [kg m/s] momentum f, F [N] force P [Pa] pressure A, W [J] work E, U, W [J] energy P [W] power T, Θ [K] thermodynamic temperature t, θ, [ C] Celsius temperature Q [J] calory,calolie C [J/K] heat capacity c [J/(kg K)] specific heat 144

154 I [A, C/s] electric current Q [C] electric charge V, φ [V] electric potential, V [V] voltage difference E [V] electromotive force R [Ω] resistance ρ [Ω m] resistivity ε [F/m] dielectric constant E [V/m] strength of electric field µ [H/m] permeability H [A/m] strength of magnetic field L, M [H] inductance C [mol/l] molarity 145

155 ,,.,. A :.. [ ].. ( ) α α, α, α β β, β, β γ γ, γ δ ε ε η η : ; η = 80 % θ, θ : ; θ = 60 λ λ ( ) : ; λ = 4.0 [m] µ µ µ : ; µ = 0.5 ( ( 10 6 [m] ), ( 10 6 ) ) ν ν π π : π = ρ ρ σ σ τ τ φ φ : φ = { } ω ω (.). t = t 2 t 1 Π ( ) Σ ( ) Φ Φ Ω [Ω] : ( ) a b c c 146

156 d d (distance), d (diameter) e e : e = [C] f f (frequency) g g (gravity) : g = 9.8 [m/s 2 ] g [g] : ( (gram) ) h h (height) i i : i = 1 ( ) j i j : j = 1 ( ) j k k : k = [J/K] l l (length) m m (mass) [m] : ( (meter) ) [m 2 ] : ( ) [m 3 ] : ( ) n n (numbers) q q (electric charge) : ; q = [C] r r (radius) s [ s ] : ( (second), ) t t (time) : ; t = 3.5 [ s ] t : ; t = 50 [ C] v v (velocity) x y z A B C D E F G H I J [A] : ( (ampere) ) Φ S B C. [cal] [ C] : (Celsius) : ; 15 [ C] [C] : ( (coulomb) ) Q S D E (Electric field) E (Electromotive force) F (Force) G (Gravitation) H I I = (Impulse) [J] : ( ) 147

157 K [K] : ( ) : ; 300 [K] L L M M (mass) M (mutual inductance) N N, [N] : ( ) O O P P (pressure) P (power) P = Q Q (electric charge) : ; Q = 10 [C] Q : ; Q = 500 [J] R N R : ; R = 100 [N] R : ; R = 200 [Ω] S S : ; S = 40 [m 2 ], S : ; S = 50 [N] T S T T : ; T = 300 [K] U U V V (voltage), V (voltage difference) [V] : ( (volt) ) W W (weight) X : ; X ray, X 148

158 149

159 (1) = = 3 10 (2) = = 1 (3) 1 a 1 b = 1 a b (4) y x w z = y x z w = y z x w 1 (5) (6) (7) 2 a b 2 b c a = 1 a b c a = b a x 2 a c y = b b a x 2 = x a 2 b c y a c = b 2 c a 2 b b a c y a 2 c x 2 y x a 2 b c a c y = x a b y (1) = = = (2) = = = = 22 5 (3) q p + s r = q r p r + s p r p = q r+p s p r (4) h g j i = h i g i j g i g = h i g j g i (5) 1 x x+1 = (x+1) x x+1 (6) (7) (8) 1 a+1 1 a 1 = 1 x+1 (a 1) (a+1) = (a+1) (a 1) 2 = (a+1) (a 1) 2 a b c x 2 3 b c a x 2 = 2 a a 3 b c b c b c x2 a a x 2 b c = 2 a2 3 b 2 c 2 a b c x a b a 2 b = 4 a 3 b 12 a 2 b 2 3 (1) I = V R I R = V R = V I I = 0.3 [A], V = 3 [V] (2) b x 3 = 4 x c c (b x 3) = 4 x b c x 3 c = 4 x R = = 10 [Ω] b c x + x = 3 c + 4 (b c+1) x = 3 c + 4 x = 3 c+4 b c+1 (3) b x + 3 = c x b b x c x = b 3 (b c) x = (b+3) x = b+3 b c (4) b x 3 = 4 c x c c (b x 3) = 4 c x b c x 3 c = 4 c x b c x + c x = 3 c + 4 (b+1) c x = 3 c + 4 x = 3 c+4 (b+1) c 3 x (5) a (3 x+c) = 4 b 4 a b c (4 a b c) 3 x = 4 b a (3 x+c) 12 a b x 3 c x = 12 a b x + 4 a b c 3 c x = 4 a b c x = 4 a b c 3 c (6) b c = 1 x+1 (b c) (x+1) = 1 (b c) x + (b c) = 1 (b c) x = 1 b + c (7) a x = x2 a x (a x) (a x) = x 2 a 2 2 a x + x 2 = x 2 a 2 2 a x = 0 = 4 a b 3 x = 1 b+c b c a 2 = 2 a x x = a2 2 a = a 2

160 (1) x 2 = 1 4 ( x > 0 ) { x = a t 1 (2) y = b t 2 1 x = 4 = 1 2 (2) 10 = 5 x 100 = 25 x x = = 4 (3) 3 = x 5 9 = x 5 x = 14 (4) y 2 = x+3 (y 2) 2 = x+3 y 2 4 y+4 = x+3 x = y 2 4 y+1 (5) y = c x y 2 = c 2 x z (6) y = x y 2 = z x x = y2 c 2 x y 2 = z x = z y 2 1 (7) = 2 x 1 1 x 1 = 4 1 = 4 (x 1) x = 5 4 (8) x 2 = 1 z 2 y ( x > 0, y > 0, z > 0 ) 1 1 x = z 2 y = 1 y y = y = z 2 z z 1 (9) f = f 2 = 2 π L C 1 4 π 2 L C c f 2 = 1 4 π 2 L 5 { x = 2 t 1 (1) y = 4 t 2 c = 1 t = x 2 2 y = 4 x 2 y = 2 x 1 4 π 2 f 2 L 1 t = x a 2 y = b x a v = g t (3) y = 1 2 g t2 (4) (5) y = b a x t = v g 2 y = 1 ( ) 2 v 2 g y = v2 g 2 g { x = 2 t 1 1 y = 4 t t t = x ( ) 2 x+1 y = x y = x x x y = x x + 7 { x = t a 1 y = 3 t + b 2 1 x 2 = t a t = x 2 + a 2 6 y = 3 ( x 2 + a ) + b y = 3 x a + b (1) 1 R = = = 5 60 = 1 12 R = 12 [Ω] (2) 1 R = 1 R R 2 = R 2+R 1 R 1 R 2 = R 1+R 2 R 1 R 2 R = R 1R 2 R 1 +R 2 (3) 1 R = 1 a a = a = 3 2 a R = 2 a 3 [Ω]

161 (1) I 1 = E R 1, I 2 = E R 2, I 3 = E R 3 (2) I = I 1 + I 2 + I 3 (3) I = E R (4) I = E + E + E ( 1 =E ) R 1 R 2 R 3 R 1 R 2 R 3 ( E 1 (5) R = E ) R 1 R 2 R 3 1 R = R 1 R 2 R 3 (6) 1 R = = 6 30 = 1 5 R = 5 [Ω] 1 (7) R = 1 a + 1 b b = 4 a+3 b 3 a b R = 3 a b 4 a+3 b [Ω] 1 (1) 1 a = 1 b + 1 c + 1 d a = b c d b c+b d+c d (2) P V = w M R T (3) (4) M P V = w R T M = w R T P V 1 a + 1 b = 1 f 1 b = 1 f 1 a = a f f a b = a f a f 4 b x+c = 2 b x+c 4 ( b x+c) = 2 (b x+c) = c d+b d+b c b c d = a f a f 4 b x + 4 c = 2 b x + 2 c 2 c = 6 b x x = 2 c 6 b = c 3 b (5) a+2 = x b+x (a+2) (b+x) = x a b + 2 b + a x + 2 x = x a x + x = a b 2 b (a+1) x = (a+2) b x = (a+2) b a+1 l 2 T = 2 π g T 2 = 4 π 2 l g g T 2 = 4 π 2 l 3 F x = 1 2 m v2 v 2 = 2 F x m g = 4 π2 l T 2 v = 4 W = 1 2 Q V 1 Q = C V (1) W = 1 2 C V V = 1 2 C V 2 2 F x (2) 2 V = Q C 1 W = 1 2 Q Q C = Q2 2 C 5 M a = M g T 1 m a = T m g 2 m (1) 2 T = m a + m g 1 M a = M g (m a + m g) M a + m a = M g m g (M m)g (M +m)a=(m m)g a= M +m (2) 1 m M m a = M m g m T 1 2 M M m a = M T M m g = M m g m T M T + M m g MT +mt = 2Mmg T = 2Mmg M +m

162 (1) = = 5 5 = 3125 (2) ( 6 2 ) 3 = = 6 6 = (3) = = 7 2 = 49 (4) = = 9 2 = = 1 ( ) (5) = = (6) = =10 1 = = 10 (7) = 10 5+( 2) = 10 3 = 1000 (8) =10 3 ( 2) =10 5 = (1) a 3 a = a 3 a 1 = a 3+1 = a 4 (2) a 4 a 3 a 2 = a 4 3+( 2) = a 1 = 1 a 1 = 1 a (3) a 2 a 5 = a 2 5 = a 3 = 1 a 3 (4) ( a b 2) 3 ( a 2 b ) 2 = ( a b 2 ) 3 (a 2 b) 2 = a3 b 6 a 4 b 2 = b4 a (5) 4x 2 ( 2xy 3) 2 = 4x 2 4x 2 y 6 = 16x 4 y 6 (6) 5a 3 3a 4 =15a 3+( 4) =15a 1 = 15 a (7) 28a 2 ( 7a 3) = 28a2 7a 3=4a2 ( 3) =4a 5 ( (8) a 4 ) 3 = a 4 3 = a 12 ( (9) a 2 ) 3 = a ( 2) 3 = a 6 = 1 a 6 (10) a 5 a 0 = a 5+0 = a 5 3 a 3 a 3 (1) = a 3+( 3) 1 = a 1 = 1 a a ( (2) a 3 ) 2 ( a 4 ) 3 = a 6 a 12 = a 6 ( (3) a 2 b 1) 2 = a 4 b 2 = b2 a ( 4 6 x 2 y ) 2 (4) 9 x 3 y 3 = 36 x4 y 2 9 x 3 y 3 = 4 x y (5) 15 a 2 b 3 c ( 5 a b c 2 ) 2 = 15 a2 b 3 c 25 a 2 b 2 c 4 = 3 b 5 c 3 4 (1) 3 a 3 b 2 ( 2 a b 2) 3 6 a 3 b 2 = 3 a3 b 2 8 a 3 b 6 6 a 3 b 2 = 4 a 3 b 6 = 4 a3 b 6 (2) ( 2 x y 2) 3 6 x 4 y 2 = 8 x3 y 6 6 x 4 y 2 = 4 y4 3 x 60 a 2 (3) 7 b c 48 a3 c 3 ( ) 2 a c b 3 5 b 2 (4) 60 a2 = 7 b c ( 7 a 2 b ) 2 35 b3 48 a 3 c 3 4 a2 c 4 21 x 3 y 3 3 x2 y 35 (a b 2 ) 2 25 b 4 = a b 2 = 49 a4 b 2 21 x 3 y 3 3 x2 y 35 a 2 b 4 = a 2 5 b 2 x y 2 5 V = π r 2 h ( ) b V 2 2 = π a r a b h 6 = π b4 a 2 r2 a b h = b3 a π r2 h V V = b 3 a π r2 h π r 2 h (1) 4470 = (2) = (3) = (4) = (5) = (1) = = b3 a (2) = (3) = 4200 (4) = 2738 (5) =

163 (1) = 4.8 ( ) ( ) = ( 3) = (2) = ( ) 3 = = (3) = ( ) ( ) = = = (4) = ( ) ( ) 3 = ( ) ( ) = ( 6) = = = ( (5) ) 2 ( ) 2 = ( ) ( ) = ( 6) = = 16 1 = ( (6) ) 3 ( ) 6 = ( ) ( ) = ( ) = ( ) 3 = = = (1) 2 49 = 49 = 7 (2) = 4 3 = 4 (3) = 3 4 = 3 (4) = 2 5 = 2 (5) 3 64 = 3 ( 4) 3 = 4 (6) 5 1 = 5 ( 1) 5 = 1 11 (1) = 10 4 (2) = 15 7 (3) 5 34 = (4) = 2 4 = (5) = = = 3 3 (6) = = = a 3 = 125 a = = = ( 5 3) 1 3 = = 5 1 = 5 [cm] 1 l R = ρ S = ( ) ( ( ) ( ) = 3.14 ( ) = = = = 5.4 [Ω] 2 ( ) ( ) ) 2 9 ( ) 200 = ( ) ( ) = = [ ] = = = [s]

164 ( ) = = = [cm 3 ] [m] = ( ) [km] = ( ) 10 3 = = [km] 5 ( ) ( ) 100 = ( ) ( ) 10 2 = = = 2.34 [%] 6 ( ) ( ) = ( 31) = = [ ] 3 1 (1) (2) (3) (4) (5) (6) (7) (8) (1) 2555 [g] = [kg], 10.50, , 2.555, = [kg] (2) 1.253, , , 0.525, 3.12, = [m] (3) [m] = [cm], 20.25, 1.237, , 1.237, 0.323, = [cm] 3 (1) 5.2 [mm] = [m], V = = V = [m 3 ] (2) V = 4 3 π r3 = (10.00)3 = V = 4189 [cm 3 ]

165 (1) (0.50) = ,, = [m 2 ] (2) (, ) = ,, = [cm 2 ] (3) (10.00) = ,, = [cm 2 ] (1) 127, , 9.7, = (2) = ,,, = (3) = (4) 14 = (5) = = = [m] [ma] = [A], V = R I = = [V] P = R I 2 = 6.00 (0.0101) 2 = [W] 4 Q = N e N = Q e, 1 e = [C], 1 N = (, 1 1 1) = = = [ ] 2 e = [C], 1 N = (, 1 1 1) 1 = = ( ) = ( ) [ ] 1.000[L] = [cm 3 ], , , , ( ) = = [g] = = [m]

166 (1) [ ] (2) [ ] 2 (1) 1230 [m] = [m] = 1.23 [km] (2) 450 [mm] = [mm] = ( ) 10 3 [m] = [m] = ( ) 10 6 [m] = [µm] (3) 1.2 [kv] = [V] (4) [A] = [A] = ( ) 10 6 [A] = [µa] (5) 0.56 [MΩ] = [MΩ] = ( ) 10 6 [Ω] = [Ω] = ( ) 10 3 [Ω] = [kω] 3 (1) 2.94 [km] = [m] (2) 38.4 [µm] = [µm] = ( ) 10 6 [m] = [m] (3) 457 [kg] = [kg] = ( ) 10 3 [g] = [g] (4) 9.86 [µω] = [Ω] (5) 6.31 [MΩ] = [Ω] 4 (1) [Ω] = 1.58 [µω] (2) [g] = 8.65 [Mg] (3) [m] = 2.88 [km] (4) [A] = 5.43 [ma] (5) [V] = ( ) 10 3 [V] = [kv] = 33.7 [kv] 5 (1) 1 [g] = [kg] = 10 3 [kg] 1 [cm 3 ] = (0.01) 3 [m 3 ], 20.8 [g/cm 3 ] = = ( 10 2) 3 [m 3 ] = 10 6 [m 3 ] [kg/m 3 ] = [kg/m 3 ] (2) 1 [kg] = 1000 [g] = 10 3 [g] 1 [m 3 ] = (100) 3 [cm 3 ], = 6 = ( 10 2) 3 [cm 3 ] = 10 6 [cm 3 ] [kg/m 3 ] ( ) [g/cm 3 ] = [g/cm 3 ] = 24.3 [g/cm 3 ] 40 [mm]=4 [cm], 100 [mm]=10 [cm], 10 [mm]=1 [cm], V = = 40 [cm 3 ] m = ρ V = 7.86 [g/cm 3 ] 40 [cm 3 ] = [g]

167 m = ρ V V = m ρ, 500 [g] V = 1.83 [g/cm 3 ] = [cm3 ] 8 (1) 1 [s] = [m/s] = 273 [cm 3 ] [min], 10 [m] 1 60 [min] = 600 [m/min] (2) 1 [m] = 1 1 [km], 1 [s] = [h], [m/s]= 1000 [km] = 72 [km/h] [h] 9 1 [m] = 1 1 [km], 1 [s] = [h], 100 [m] = 1000 [km] 10 [s] 10 1 =36 [km/h] 3600 [h] 10 (1) 36 [km/h]= 72 [km/h]= a = 36 km [m] =10 [m/s] 3600 [s] [m] =20 [m/s] 3600 [s] (20 10) [m/s] 10 [s] = 1 [m/s 2 ] (2) 70 [km/h]= [m] =19.4 [m/s] 3600 [s] 0 [km/h] = [m] 3600 [s] = 0 [m/s] a= (0 19.4)[m/s] = 2.8[m/s 2 ] 7 [s] 11 (1) m = 2.5 [g/cm 3 ] 8000 [cm 3 ] = [g] = [g] = 20 [kg] (2) 20 [km/h]= 92 [km/h]= a= [m] =5.6 [m/s] 3600 [s] [m] =25.6 [m/s] 3600 [s] ( ) [m/s] =4.0 [m/s 2 ] 5 [s] (3) F = m a = 20 [kg] 4.0 [m/s 2 ] 12 = 80 [kg m/s 2 ] = 80 [N] F = m a a = F m, 49 [N] a= 20 [kg] = 49 [kg m/s2 ] =2.45 [m/s 2 ] 20 [kg] 13 (1) 1 [cm 2 ] =, ( ) 2 1 [m 2 ] = 10 4 [m 2 ] [N/cm 2 ] = 1 [N] 1 [cm 2 ] = 1 [N] 10 4 [m 2 ] = 10 4 [N/m 2 ] = [N/m 2 ] (2) 1 [N]= [kn]=10 3 [kn], 588 [Pa] = 588 [N/m 2 ] = = [kn] 1 [m 2 ] 588 [N] 1 [m 2 ] = [kn/m 2 ] (3) 1 [N]= [kn]=10 3 [kn], 3500 [N/m 2 ] = 3500 [N] 1 [m 2 ] = [kn] 1 [m 2 ] = 3.5 [kn/m 2 ]

168 [kg] 9.8 [m/s 2 ] 2 2 [m 2 ] 15 = [N/m 2 ] W = ( 200 [kg] 9.8 [m/s 2 ] ) 10 [m] 16 = ( ) [N] 10 [m] = [N m] = [J] (1) 300 [J] = 300 [N m] (2) 9800 [N m] = 9800 [J] 17 P = = = 120 [N] 40 [m] 15 [s] 4800 [N m] 15 [s] 4800 [J] 15 [s] = 320 [J/s] = 320 [W] = [J] = 9.8 [kj] 18 ( 2000 [kg] 9.8 [m/s 2 ] ) 40 [m] P = 50 [s] = [kg m/s2 ] 40 [m] 50 [s] = = = [N] 40 [m] 50 [s] [N m] 50 [s] [J] 50 [s] = [J/s] = [W] = [W] = [kw] 100 [W] = 100 [J] 1 [s], 1 [s] 100 [J],. 20 (1) 8.5 [W h] = 8.5 [W] 3600 [s] = [W s] (2) 20 [W h] = 20 [W] 3600 [s] = 20 [J/s] 3600 [s] = [J] 1 (1) 0.5 [kgw] = 0.5 [kg] 9.8 [m/s 2 ] = 4.9 [kg m/s 2 ] = 4.9 [N] (2) 0.7 [kn]= [N] = (3) 800 [g] 9.8 [m/s 2 ] = 0.8 [kg] 9.8 [m/s 2 ] = ( ) [kg m/s 2 ] = ( ) [N] = [kgw]=71.4 [kgw] [kgw] = 0.8 [kgw] = [gw] = 800 [gw] 2 (1) [cal] = [J] = [J] (2) [J] = ( ) 10 3 [J] = [kj] = [kcal] = [kcal] (3) 0.4 [kcal] = [cal] = ( ) 4.2 [J] = [J]

169 [m] 45 [m/s] = = [km] 1 [s] 1 [s] ( ) [km] = 3600 [s] ( ) [km] = 1 [h] = 162 [km/h] 162 [km] = 2.5, [km] 2.5 [h] 40 [km/h] =, a = 4 = [km/h] 40 [km] 1 [h] = [m] 3600 [s] = [m/s] [m/s] 4 [s] = [m/s2 ] = 2.8 [m/s 2 ] 1.00 [m]=100 [cm], 2.00 [m]=200 [cm], 2.00 [mm]=0.200 [cm],, 100[cm] 200[cm] 0.200[cm] 7.86[g/cm 3 ] = [g] = [kg], [kg] 9.8 [m/s 2 ] = 308 [kg m/s 2 ] = 308 [N] 5 50 [cm] = 0.5 [m], 20 [cm] = 0.2 [m], 2 [t] = 2000 [kg],, 2000 [kg] 9.8 [m/s 2 ] 0.5 [m] 0.2 [m] = [kg m/s2 ] 0.1 [m 2 ] = [N] 0.1 [m 2 ] = [N/m 2 ] = [Pa] = 196 [kpa] 6 ( 10[m 3 ] 1000[kg/m 3 ] ) 9.8[m/s 2 ] 100[m] 1 [s] = [kg] 9.8 [m/s2 ] 100 [m] 1 [s] = [kg m/s2 ] 100 [m] 1 [s] = = = [N] 100 [m] 1 [s] [N m] 1 [s] [J] 1 [s] = [J/s] = [W] = 9800 [kw] 7 F = m a = 30 [kg] 12 [m/s] 5 [s] = 30 [kg] 2.4 [m/s 2 ] = 72 [kg m/s 2 ] = 72 [N]

170 = 9 = 3, sin θ = 3 5, cos θ = = 64 = 8, sin α = 15 17, cos α = = 28 = 2 7, sin β = 6 8 = 3 4, cos β = a 4 = sin 30, a = 4 sin 30 = = b b = = tan 30, tan 30 = θ = 0 sin 2 0 +cos 2 0 = = 1, tan α = 15 8 = 7 4 = = 6 θ = 30 ( ) 2 ( ) sin cos 2 30 = + =1 2 2 θ = 45 ( ) 2 ( ) sin cos 2 45 = + =1 2 2 θ = 90 sin cos 2 90 = = 1, sin 2 θ + cos 2 θ = 1. 4 (1) tan 38 = (2) cos 60 = (3) sin 75 = (4) tan 53 = (5) cos 8 = (1) sin θ = θ 19 (2) cos θ = θ 32 (3) tan θ = 2.36 θ 67 6 (1) sin 43 = cos 25 = tan 86 = (2) sin 37 = , cos 37 = , sin cos 2 37 = (0.6018) 2 + (0.7986) 2 = (3) cos 40 = , sin 50 = cos 40 = sin 50 sin 70 = , cos 20 = sin 70 = cos 20 BAC = = 60, 2 x = 20 tan 60 = = [m] (1) BD = AB sin BAD = 18.0 sin 34 = = 10.1 [m] (2) DBA = = 56, DBC = = 10 AC = AD + DC = 18.0 cos tan 10 = = 16.7 [m] S = AC BD 1 2 = = 84.3 [m2 ] BD (3) = cos CBD, BC 10.1 = cos 10 BC BC = 10.1 cos 10 = 10.1 = 10.3 [m]

171 (1) CAD = 90 C = B, ACD BAD, DC AD = DA, BD = x, BD 13 x = 6 6 x x (13 x) = 36 x 2 13 x + 36 = 0 (x 4) (x 9) = 0 x = 4, 9 AB>AC BD>DC x = 9 BD = 9, CD = 13 9 = 4 (2) AB = BD 2 + DA 2 = = 117 = 3 13 cos θ = BD AB = = 3 = a = b tan 39 1 a = (b+30.0) tan , 2, b tan 39 = (b+30.0) tan 27 b tan 39 = b tan tan 27 b (tan 39 tan 27 ) = 30.0 tan 27 5 BD = b, h = b tan β h = (b+a) tan α 1, 2, b tan β = (b+a) tan α 1 2 b tan β = b tan α + a tan α b (tan β tan α) = a tan α b = 1, h = = a tan α tan β tan α a tan α tan β tan α tan β a tan α tan β tan β tan α b =, 30.0 tan 27 tan 39 tan 27 = = = 51.0 [m] 0.30 a = 51.0 tan 39 = = 41.3 [m]

172 , d + b = a, a b = d d d + b = a,. 2 3 ABC, (1) BC + CA = BA (2) AB AC = AB + CA = CA + AB = CB (3) AC BC = AC + CB = AB 4 ( (1) 2 3 ) a = 6 a (2) 2 a + 3 a = 5 a (3) 4 b b = 3 b ( (4) 3 a ) ( + b 2 a ) 2 b = 3 a + 3 b 2 a + 4 b = a + 7 b 5 a = (3, 2), b = ( 2, 1), (2) 3 b = 3 ( 2, 1) = ( 6, 3) 3 b = ( 6) = 3 5 (3) 2 a 3 b = 2 (3, 2) 3 ( 2, 1) 2 a 3 b = (6, 4) ( 6, 3) = (12, 7) = ( 7) 2 = 193 (4) a + 2 b = (3, 2) + 2 ( 2, 1) a + 2 b = ( 3, 2) + ( 4, 2) = ( 7, 4) = ( 7) = 65 6 (1) AB = ( 1, 5) (4, 2) (2) (3) = ( 1 4, 5 2) = ( 5, 3) AB = ( 5) = 34 AB = (1, 4) (6, 3) = (1 6, 4 3) = ( 5, 7) AB = ( 5) 2 + ( 7) 2 = 74 AB = (2, 1) (0, 5) = (2 0, 1 5) = (2, 4) AB = ( 4) 2 = (1) F 1 = (3, 3), F 2 = ( 4, 2) (2) (1) a + b = (3, 2) + ( 2, 1) a + b = (1, 1) = ( 1) 2 = 2

173 164 6 (3) (4) F = F1 + F 2 = (3, 3) + ( 4, 2) = ( 1, 5) F = ( 1) = 26 8 a = (a1, a 2 ) = 5 cos 30, 5 sin 30 ) ( ) 3 = 5 2, ( 5 ) 3 5 =, 2 2 a 1 = 5 3 2, a 2 = { S W sin θ = 0 (1) N W cos θ = 0 { S cos θ N sin θ = 0 (2) S sin θ+n cos θ W = 0 (3) (1), S = W sin θ = 50 sin 45 2 = 50 2 = 25 2 [N] N = W cos θ = 50 cos 45 2 = 50 2 = 25 2 [N] [ ] (2) S, N 1, S = W sin θ, N = W cos θ. 10 (1) S 1 = (S 1x, S 1y ), S 2 = (S 2x, S 2y ), S 1x = S 1 sin 30 = 1 2 S 1 3 S 1y = S 1 cos 30 = 2 S 1 S 2x = S 2 sin 60 = 3 2 S 2 S 2y = S 2 cos 60 = 1 2 S 2 (2) x S S 2 = 0 3 y 2 S S 2 W = 0 (3) (2), 1 2 S S 2 = S S 2 = W S 2, 3 S 1 = 2 W S 1, S 2 = 1 2 W W=20 [N], 2=1.4, 3=1.7, 11 S 1 = S 2 = 1 2 x, V 1 sin θ + V 2 = 0 20 = 17 [N] 20 = 10 [N] sin θ = V 2 V 1 = = 0.6, θ 37, cos θ = 1 sin 2 θ = 1 (0.6) 2 = 0.64 = 0.8, t, y, V 1 cos θ t = 50 t = 50 V 1 cos θ = 50 = 125 [s]

174 , (6.0) 2 +(8.0) 2 =10.0[m/s] tan α = 8.0 = 1.3, 6.0 α 53, A 53,,, 8.0 t = 40 t = 5.0 [s], = 30.0 [m] B 30.0 [m] 1 (1) CB = CA + AB ( = ) AC + AB = AB AC (2) BC BA = ( BC ) AB = AB + BC = AC 2 ( 2 a ) ( 4 b + c 2 a ) 2 b + c 4 (1) W = W, S 1 S 2 S 2, S 1, x S 2 S1 sin 30 = 0 1 S 2 S 1 = 0 2 y S 1 cos 30 W = S 1 W = 0 (2) (1), = 2 S 1 3 W= = 3 3 S 2 = 1 2 S 1 = = [N] [N] (3) h = cos 30 3 = = [cm] 5 (1) = 2 a 8 b +2 c 2 a +4 b 2 c = 4 b 3 (1) (2) F = F1 + F 2 + F 3 = (2, 2) + (2, 2) + ( 3, 4) = (1, 4) F = = 17 (3) F = (1, 4) = 1 i + 4 j = i + 4 j (4) α, tan α = 4 1 = 4,, α 76 (2) x S cos 45 W sin 30 =0 2 2 S 1 2 W = 0 y S sin 45 +N W cos 30 = S + N 2 W = 0

175 166 7 (3) (2), S = W = 2 2 W = 2 10=5 2 [N], W + N 2 W = 0, 3 1 N = W = 10 = 5 ( 3 1 ) [N] [km/h] = 36 [m/s] = 10 [m/s] [km/h] = 54 [m/s] = 15 [m/s] (15 10) = 100 = 20 [s] (1) 2 3 = 8 3 = log 2 8 (2) 5 2 = 25 2 = log 5 25 (3) 3 4 = 81 4 = log 3 81 (4) = = log (5) = = log (1) log 9 N = 2 (2) log a 125 = 3 (3) log a 27 = = N N = 81 a 3 = 125 a = 5 a 3 = 27 a = 3 (4) log 49 N = = N 3 N = = ( 7 2 )1 2 = = 7 1 = 7 log a A B = log a A + log a B 1, B 1 B, log a A 1 B = log a A + log a 1 B ( ), 2, n, log a 1 B = log a B 1 ( ), ( ), = ( 1) log a B = log a B ( ) log a A B = log a A log a B

176 n A = A 1 n 5, log a n A = log a A 1 n log a 2 = x, log a 3 = y (1) log a 6 = log a (2 3) = 1 n log a A ( 2 ) = log a 2 + log a 3 = x + y (2) log a 3 2 = 2 log a 3 = 2 y (3) log a 1 2 = log a 1 log a 2 = 0 log a 2 = log a 2 = x (4) log a 9 8 = log a 9 log a 8 = log a 3 2 log a 2 3 = 2 log a 3 3 log a 2 = 2 y 3 x (5) log a 3 2 = log a = 1 3 log a 2 = 1 3 x (6) log a 6 = loga = 1 2 log a 6 = 1 2 log a(2 3) = 1 2 ( log a 2 + log a 3 ) = 1 2 ( x + y ) (7) log a 8 a 2 = log a 8 + log a a 2 = log a log a a 2 = 3 log a log a a = 3 x = 3 x log b a, a, 7 log b a = log a a log a b = 1 log a b log b a log a b = 1 log 2 = 0.30, log 3 = 0.48, log 7 = 0.85, (1) log 9 3 = log 10 3 log 10 9 = log 3 log 9 = log 3 log 3 2 = log 3 2 log 3 = 1 2 = 0.5 (2) log 5 14 = log log 10 5 = log 10(2 7) log = log log 10 7 log log 10 2 = = log 2 + log 7 1 log log 5 14 = 1.6 = 1.64 (3) log 2 9 log 3 4 = log 10 9 log 10 2 log 10 4 log 10 3 = log 9 log 2 log 4 log 3 = log 32 log 2 log 22 log 3 = 2 log 3 log 2 2 log 2 log 3 = 2 2 = 4

177 log 2 = , log 3 = , (1) log 200 = log ( ) = log 2 + log 10 2 = log log 10 = = (2) log = log ( ) = log 3 + log 10 4 = log 3 4 log 10 (3) log 6 = log (2 3) = = = log 2 + log 3 = = (4) log 5 = log 10 2 = log 10 log 2 9 = = (1) 5 y = 2 x, log 5 y = log 2 x y log 5 = x log 2 ( ) at 1 (2) N = b 2, ( ) at 1 log N = log b 2 ( ) at 1 log N = log b + log 2 log N = log b + a t log 1 2 [ ] log N = log b a t log , m 1 m 2 = 5 log D 1 D 2, D 1 = 10 D 2, 11 m 1 m 2 = 5 log 10 D 2 D 2 = 5 log 10 = 5 1 = log 2 = 0.30, log 3 = 0.48, log 7 = 0.85, (1) ph = log ( ) = log ( ) = log ( ) = ( 2 log 7 4 log 10 ) = ( ) = 2.3 (2) ph = log ( ) = log ( ) = log ( ) = log ( ) = ( 3 log 2+log 7 12 log 10 ) = ( ) = (3) ph = log ( ) = log ( ) = log ( ) = log ( ) = ( 2 log 3+log 7 8 log 10 ) = ( ) = 6.19

178 = 3.2, (1) 5.0 = log [H + ] log [H + ] = 5.0 [H + ] = = 10 5 (mol/l) (2) 3.5 = log [H + ] 13 log [H + ] = 3.5 [H + ] = = = = (mol/l) 0.10 = , log 2 = 0.30, 20 log P = 20 log P ( ) 1 = 20 log = 20 ( log 1 log log 10 ) = 20 ( ) = 74 [db] = 3.2, log 2 = 0.30, 20 log P P 0 = 20 log, log P = P 64 = = = 3.2 log P log ( ) = 3.2 log P ( log 2 5 log 10 ) = 3.2 log P ( ) = 3.2 log P = 1.5 P = = ( 2) = = [Pa] 1 log 2 = 0.30, log 3 = 0.48, log 7 = 0.85, (1) log 35 = log (7 5) = log 7 + log 5 = log 7 + log 10 2 = log 7 + log 10 log 2 = = 1.55 (2) log 600 = log ( ) = log ( ) = log 2 + log log 10 = = 2.78 (3) log 0.9 = log ( ) (4) log 2 9 = log 9 log 2 = log ( ) = 2 log 3 log 10 = = 0.04 = 2 log 3 log 2 = = log 32 log 2 = 3.2 (5) log 6 7 = log 7 log 6 = log 7 log(2 3) log 7 = log 2 + log = = 1.08 (6) log = log 4.9 log 3 = log ( ) log 3 = = log ( ) log 3 2 log 7 log 10 = log 3 =

179 %, 80%, 5 100, n = 3 = = ( ) n = ( ) n 4 = ( 4 log 5 ) n = log 1 5 n log 4 5 = log 1 5 log 1 5 log 1 log 5 log 4 = log 4 log 5 5 log 1 log 10 2 log 2 2 log 10 2 log 1 (log 10 log 2) 2 log 2 (log 10 log 2) = 0 (1 0.3) [ log 2=0.3] (1 0.3) = = 7 [ ] 1, 1 2, 10 2 n = , 2 n = = 10 5 log 2 n = log 10 5 n log 2 = 5 log 10 5 log 10 n = log 2 = 5 1 = 16.6 [ log 2=0.3] [ ] 4 m 1 = 2.5 log F F 0, = 2.5 log F F = 2.5 log F F 0 1, 2, log F F 0 = 1 1 log F F 0 = log F log F 0 = 1 1 log F log F 0 = , 5 log F log F = 7 5 log F F = F F = = = = = = 25 [ ] 5.1 = log [H + ] log [H + ] = 5.1 [H + ] = = = [ = 2.5 ] = (mol/l) [ = 7.9 ]

180 log P 1 P 0 = 100, log P 1 P 0 = log P 2 P 0 = 40, log P 2 P 0 = log P 1 log P 0 = log P 2 log P 0 = log P 2 log P 1 = 3 7 G = 20 log V 0 V i, 40 = 20 log 1 V i, log 1 V i = 2 1 V i = 10 2 = 100 V i = 1 = 0.01 [V] 100 log P 2 P 1 = 3 P 2 = 10 3 P 1 ( ) n 80, = 10 3, 100 ( ) n 4 = ( ) n 4 log = log n log 4 5 = 3 log 10 3 log 10 3 log 10 n = log 4 = log 4 log log 10 = log 2 2 log log 10 = 2 log 2 (log 10 log 2) = 3 log 10 3 log 2 log 10 = = 30 [ ]

181 (1) 480 = = α = 120 (2) 150 = = ( 1) α = 210 (3) 740 = = α = 20 (4) 1230 = = ( 4) α = (1) 380 = = < 20 < 90, 1 (2) 250 = = ( 1) 90 < 110 < 180, 2 (3) 180 < 235 < 270, 3 (4) 420 = = ( 2) 270 < 300 < 360, 4 3 tan θ = y x ( x 0 ), 1 x > 0, y > 0 tan θ > 0 2 x < 0, y > 0 tan θ < 0 3 x < 0, y < 0 tan θ > 0 4 x > 0, y < 0 tan θ < 0 4, θ =315, x > 0, y < 0, sin 315 = y r = 1 2 r r 1 2 cos 315 = x r r = r tan 315 = y 1 r 2 x = 1 2 r = 1 2 = 2 2 = 1 2 = 2 2 = 1, r > 0, x 0, y tan θ = y x = r x = sin θ cos θ r., 0 < θ < 90 θ, 180 θ 2, sin(180 θ) = sin θ cos(180 θ) = cos θ tan(180 θ) = sin(180 θ) cos(180 θ) = sin θ cos θ = sin θ cos θ = tan θ, 0 < θ < 90 θ, θ 3, sin(180 + θ) = sin θ cos(180 + θ) = cos θ tan(180 + θ) = sin(180 + θ) cos(180 + θ) = sin θ cos θ = sin θ cos θ = tan θ

182 8 173, 0 < θ < 90 θ, 360 θ = 180 +(180 θ) 4, sin(360 θ) = sin{180 +(180 θ)} = sin(180 θ) = sin θ cos(360 θ) = cos{180 +(180 θ)} = cos(180 θ) = ( cos θ) = cos θ tan(360 θ) = sin(360 θ) cos(360 θ) = sin θ cos θ = sin θ cos θ = tan θ, sin 315 = sin( ) 2 = sin 45 = 2 cos 315 = cos( ) 2 = cos 45 = 2 tan 315 = tan( ) = tan 45 = 1. 5 (1) 2 θ (90 < θ <180 ), 180 θ = θ θ = 180 θ θ 1 (0 <θ <90 ), { sin θ = sin(180 θ ) = sin θ sin θ = 0.40 sin θ = 0.40, θ 24 cos θ , tan θ cos θ = cos(180 θ ) = cos θ tan θ = tan(180 θ ) [ ] 4 = tan θ [ ] 2, tan θ = sin θ cos θ sin2 θ+cos 2 θ =1, sin θ = 0.40, (0.40) 2 + cos 2 θ = 1 cos 2 θ = 0.84 cos θ = ± 0.84 θ 2 cos θ < 0, cos θ = 0.84 cos θ 0.92, tan θ = [ ],. (2) 4 θ (270 < θ <360 ), 360 θ = θ θ = 360 θ θ 1 (0 <θ <90 ), 4, tan θ = tan(360 θ ) = tan θ, tan θ = 2.00, tan θ = 2.00, tan θ = 2.00 θ 63 sin θ , cos θ , 4, sin θ = sin(360 θ ) = sin θ cos θ = cos(360 θ ) = cos θ [ ] 4, tan θ = sin θ cos θ sin2 θ+cos 2 θ =1

183 174 8, sin 2 θ cos 2 θ + cos2 θ cos 2 θ = 1 cos 2 θ tan 2 θ + 1 = 1 cos 2 θ. tan θ = 2.00, ( 2.00) = 1 cos 2 θ cos 2 θ = 1 cos θ = ± θ 4 cos θ > 0, cos θ = 1 cos θ , = sin θ 1 5 sin θ = (1) sin 115 = sin( ) = sin (2) cos 223 = cos( ) (3) 38 = = ( 1), , tan( 38 ) = tan 322 = cos = tan( ) = tan 38 [ 4 ] (4) 403 = = , , cos 403 = cos (5) 412 = = ( 2), , sin( 412 ) = sin 308 = sin( ) = sin 52 [ 4 ] (6) 949 = = , , tan 949 = tan 229 = tan( ) [ ] 4 = tan (1) 2 π = π 6 [rad] (2) 2 π = π 4 [rad] (3) 2 π = π 3 [rad] (4) 2 π = π 2 [rad] (5) 2 π = 3 2 π [rad] (6) 2 π = 5 2 π [rad] 8 (1) (2) (3) π 6 = 360 π 6 2 π = 30, sin π 6 = sin 30 = 1 2 π π 4 = cos π 4 = cos 45 = 2 π = 45, 2 2 π 2 2 π = 90, π 2 = 360 sin π 2 = sin 90 = 1

184 8 175 π π (4) 3 = π = 60, tan π 3 = tan 60 = 3 (5) 5 π = π 2 π = 900, 900 = , 5 π [rad] 900,, 180, cos 5 π = cos 900 = cos 180 = 1 (6) 4 3 π = π = 240, 2 π 240 = = ( 1), 4 3 π [rad] 240,, 120, tan ( 43 ) π = tan( 240 ) = tan 120 = tan( [ ] ) 4 = tan 60 1 = 3 (1) 24 = = ( 1), , 4, 24 = 2 π = 2 15 π [rad]. sin( 24 ) = sin 336 = sin( ) = sin 24 [ 4 ] cos( 24 ) = cos 336 = cos( ) = cos 24 [ 4 ] tan( 24 ) = tan 336 = tan( ) = tan 24 [ 4 ] (2) 481 = = , , 2, 481 = 2 π = π [rad]. sin 481 = sin 121 = sin( ) [ ] 4 = sin cos 481 = cos 121 = cos( ) [ ] 4 = cos tan 481 = tan 121 = tan( ) [ ] 4 = tan (3) 3 π [rad] 4 = π 2 π = 240, 3. sin 4 3 cos 4 3 tan 4 3 π = sin 240 = sin( ) [ ] 4 = sin 60 3 = 2 π = cos 240 = cos( ) [ ] 4 = cos 60 = 1 2 π = tan 240 = tan( ) [ ] 4 = tan 60 = 3

185 176 8 (4) 13 4 π [rad] = π 2 π = 585, 585 = = ( 2), , 2. ( sin 13 ) 4 π = sin( 585 ) = sin 135 = sin( [ ] ) 4 2 = sin 45 = ( 2 cos 13 ) 4 π = cos( 585 ) = cos 135 = cos( [ ] ) 4 2 = cos 45 = ( 2 tan 13 ) 4 π = tan( 585 )= tan 135 = tan( [ ] ) 4 = tan 45 = 1 (5) ( ) π [rad] = 11 6 π [rad] 11 = π 2 π = 330, 4 (. sin 3 7 ) π = sin = sin( ) = sin 30 = 1 ( 2 cos 3 7 ) π = cos ( tan = cos( ) 3 = cos 30 = 2 ) π = tan 330 = tan( ) 3 = tan 30 = 3 [ ] 4 [ ] 4 [ ] 4 2 (1) 2 θ (90 < θ <180 ), 180 θ = θ θ = 180 θ θ 1 (0 <θ <90 ), sin θ = sin(180 θ ) = sin θ 3 sin θ = sin θ , θ 30 cos θ , tan θ cos θ = cos(180 θ ) = cos θ tan θ = tan(180 θ ) [ ] 4 = tan θ [ ] 2, tan θ = sin θ cos θ sin2 θ+cos 2 θ =1, ( ) sin θ = 2, + cos 2 θ =1 2 cos 2 θ = 1 cos θ = ± θ 2 cos θ < 0, cos θ = 1 2, tan θ = = 3 (2) 4 θ (270 < θ <360 ), 360 θ = θ θ = 360 θ θ 1 (0 <θ <90 ), 4, { cos θ = cos(360 θ ) = cos θ cos θ = , cos θ = , θ 65

186 9 177 sin θ , tan θ , 4, 3 sin θ = sin(360 θ ) = sin θ tan θ = tan(360 θ ) = tan θ θ sin 2θ θ sin 2θ θ sin 2θ θ sin 2θ θ sin 2θ θ sin 2θ θ 360 sin 2θ (1) (2) k = w l = = 4.3 [N/m] (3) w = 1.00 [N], w = 4.3 l l = w 4.3 = 1.00 = [m] = 23.3 [cm] (1) (2) 20 [ C] 100 [ C] 2, α = = = [1/K] [1/K] (3) t [ C] l, 20[ C] l 0, { l = l (t 20) }

187 178 9 (4) 0 [ C] [cm], =l 0 { 1+(0 20) } l 0 = = , 500 [ C], l= { 1+(500 20) } = = [m] = [cm] 3 (1) [cm] 500 [ C], ρ = {1+(500 20) } 4 = = [µω cm] (1) y = x (6 x) = x x (2) y = x x = ( x 2 6 x ) = { (x 3) 2 9 } = (x 3) p = 3, q = 9 x=3[m], 9[m 2 ] (3) x=1 [m] y = =5[m 2 ] (4) x=2 [m] y = =8[m 2 ] x=3 [m] y = =9[m 2 ] x=4 [m] y = =8[m 2 ] x=5 [m] y = =5[m 2 ] x=6 [m] y = =0[m 2 ] (2) 20 [ C] 100 [ C] 2, k = = = [1/K] [1/K] (3) t [ C] ρ, 20 [ C] ρ 0, { ρ = ρ (t 20) } (4) 0 [ C], ρ = {1+(0 20) } = = [µω cm] 5 (1) y = x (40 2 x) = 2 x x (2) y = 2 x x = 2 ( x 2 20 x ) = 2 { (x 10) } = 2 (x 10) p = 10, q = 200 x = 10 [cm], 200 [cm 2 ]

188 9 179 (3) x = 2 [cm] y = = 72 [cm 2 ] x = 4 [cm] y = = 128 [cm 2 ] x = 6 [cm] y = = 168 [cm 2 ] x = 8 [cm] y = = 192 [cm 2 ] x = 10 [cm] y = = 200 [cm 2 ] x = 12 [cm] y = = 192 [cm 2 ] x = 14 [cm] y = = 168 [cm 2 ] x = 16 [cm] y = = 128 [cm 2 ] x = 18 [cm] y = = 72 [cm 2 ] 1 (1) 83 2 = [N/m]. (2) 6.0 [N] 166 [N/m] = [m] = 3.6 [cm], W [N],. 2 (4) 3 k = w x = = [N/m] F = 170 x 14.0 = 170 x, x = = [m] 8.2 [cm]

189 ( ) n n MKS MKSA ( ) ( ) cos ( ) sin CGS ( )

190 tan ( ) ( ) ( ) db( ) rad( ) log ( ) ( ) ph ph (2 ) ( ) ( )

191 182

192 ( ) 2018

193

194 ,, ,,. 3.,,. 4...,.,.,,. 30 4

195

196 1 187

197 1.. (1) = (2) = (3) = (4) = (5) a 2 a 5 = (6) = (7) = (8) = (9) = (10) = 2.. (1) (2) (3) (4) (5) (6) 1 a 2 3 = b a + 1 b = 2 a 9 2 = b a + c d = 1 a 2 5 = b a c b = 188

198 3.. (1) b a c x b c y x = (2) 36 x2 z 2 27 a 2 b = (3) a b c d e b = (4) a x 2 y z b x z = (5) 1 a 1 + a = (6) 1 x x 1 = (7) 1 3 x y x 2 y = 4.. (1) b a c b = (2) b a b y a x y x = (3) b a + 2 a 3 b 3 a 5 b = 189

199 5.. (1) = (2) a b + c e b d = (3) 1 a 1 b + 1 c = (4) a + b c c d = (5) b a a d b c = (6) 1 1 a 1 b = 6. x =. (1) x a + x b = 1 c (2) a x 4 = c x b (3) 3 b x + 5 = 2 b x + c (4) x 2 = 3 4 x 2 (5) 2 x 3 x c = 5 7 (6) 1 1 x + 1 y = c x + y (7) x x + 2 = 1 2 (8) 3 x + y = y 190

200 7. [ ]. (1) b a + 1 b = 1 2 [ a = ] ( b 2) (2) a x + b = c x + 2 [ x = ] ( a c) (3) x a = x b + 1 [ x = ] ( b 0) (4) 1 a = 1 x + 1 y + 1 z [ a = ] (5) 2 = 1 a 1 [ a = ] (6) x + y = a y + b [ y = ] ( a 1) (7) b x a + c y b = 1 2 [ a = ] ( b 2 c y ) (8) a 2 b y = x 2 b y c 2 [ x = ] ( x 0) (9) x + b c y = c x d y [ c = ] ( b y x) (10) x + 2 = a [ x = ] (11) 1 x + 1 = y 5 [ x = ] (12) 1 2 m v2 = 1 2 m v m g h [ v = ] ( v > 0) (13) a 2 b 2 a 2 c + 2 c b = 1 [ b = ] (14) d e = 1 a + 1 [ a = ] ( d e) (15) a 2 = c + 3 [ c = ] (16) 1 a 1 = 3 [ a = ] 191

201 8. 2 x, b =. { (1) a = 2 x 1 b = 4 x x + 3 (2) { a = x a b = 3 x + d 9. 2 x, y., b + c e 0. { a = b x + c y d = e x y M = a x + y 1, Q = b M c x 2,. (1) b M, Q, a, c, y. M 0, a 0. (2) y Q, a, b, c, x. b v y = g t 1, y = 1 2 g t2 2,. (1) 1 t =. (2) (1) t 2, v y =. 192

202 2 193

203 1.. (1) = (2) (3 2 ) 3 = (3) = (4) a 2 b 3 c 2 ( a b c) 2 = (5) ( a 2 b 3 ) 2 = (6) (y 2 ) 3 y 2 = (7) = (8) (2 a b) 2 a b 3 = (9) 2 x 2 y 3 x 3 y 2 = (10) 3 a 2 b 3 (2 a 2 b) 2 = 2.. (1) 36 x2 z 2 27 a 2 b 2 57 a b c 56 x y 2 z 3 = (2) ( 2 a 2 b) 3 = (3) ( 3 a b) 2 ( 2 a 3 b) = (4) ( 3 x 3 y 2 ) 2 ( 3 x y 3 ) 3 = (5) (9 a 3 b c 8 a b 2 c a b c 3 ) ( 6 a b c) = 194

204 3.. (1) = (2) (2 2 ) 3 = (3) ( ) = 2 (4) a 3 a 2 = (5) ( a b c) 2 (a 2 b) 2 = (6) 2 x 2 y 6 x y 2 (7) (x 3 ) 2 x 3 = (8) (a 2 b 1 ) 2 = (9) (8 a b 2 ) 2 (2 a b c) 3 = (10) 4 a 2 b ( 2 a b) 3 ( 2 b c 2 ) 2 = 4.. (1) x y 2 (x 2 y) 2 = (2) x 0 x 5 x 2 = (3) (x 2 y 1 ) 2 = (4) (2 a b 2 ) 2 6 a 4 b 2 = 195

205 5. a 10 n ( 1 a < 10, n ). (1) = (2) = (3) = (4) = 6. a 10 n ( 1 a < 10, n ). (1) = (2) = (3) 2 10 = (4) 30 4 = (5) = (6) = (7) = (8) = (9) ( ) 2 ( ) 2 = (10) = 196

206 7.,. (1) = (2) = (3) = (4) x 2 x 5 = (5) 8 a 2 b 3 ( 2 b 2 c) 2 = (6) = (7) = (8) 7 16 = (9) = (10) = 197

207 8.. (1) = (2) { ( ) 4 3 } = (3) a 3 2 a 2 a 1 4 = (4) 3 5 a 1 3 b 2 3 c a 2 3 b 1 3 c 1 2 = (5) = (6) 4 ( 4) 4 = (7) = (8) 3 a 4 3 a 5 = 198

208 3 199

209 1.. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 0.60 (12) ,. (1) 21.5 [cm] [cm] = (2) 9.8 [kg] 4144 [ g ] = (3) 3.24 [m 2 ] [m 2 ] = (4) 18.2 [mm] 16 (5) 2.0 [cm] (, π = ) 200

210 3.,. (1) 9844 [ g ] [kg] = (2) 144 [mm] [m] = (3) [mm] [cm] [m] = (4) = (5) 40.0 [cm] (, π = ) 4.,. (1) 5.42 [m 2 ] [m 2 ] = ( ) [m 2 ] (2) 9.6 [kg] 4055 [ g ] = ( ) [kg] (3) = ( a 10 n ) (4) 4.0 [cm] (, π = ) (5) [kg] [ g ] [ g ] [kg] = ( ) [kg] (6) = ( a 10 n ) 5.,. (1) [m] [cm] [mm] (2) = (3) = 201

211 6. ( ), km. 420 km,.. 7.,, 10.1 [cm], [mm], [m], 1.0 [m], [cm],., π = A, B, C, D 4. A [kg], B [ g ], C [ g ], D [kg]. 4,. 9., 4.06 [cm], 21 [cm] S [cm] S 2, S. 10., 2.08 [cm], 12 [cm] S 1, 1.25 [cm], 6.9 [cm] S 2, S. 202

212 4 203

213 1.,, ( ). (1) ( ) (2) ( ) (3) θ ( ) (4) β ( ) (5) π ( ) 2. [ ]. (1) 48.2 [µm] = ( ) [cm] (2) [A] = ( ) [µa] (3) [MΩ] = ( ) [Ω] (4) [g] = ( ) [kg] (5) [V] = ( ) [kv] 3.,. (1) 20 [kv] = ( ) [MV] (2) 50 [mg] = ( ) [g] (3) 365 [kω] = ( ) [Ω] (4) 3 [m] = ( ) [cm] 204

214 (5) 25 [km] = ( ) [m] (6) 0.9 [V] = ( ) [mv] (7) 40 [kv] = ( ) [MV] (8) 600 [kω] = ( ) [Ω] (9) 25 [mg] = ( ) [g] (10) [A] = ( ) [µa] (11) f = 50 [khz], T = ( ) [ s ] f [Hz] 1 f, 1 T [s]., f T,, T = 1 f., f = 50 [Hz], T = 1 = 0.02 [s], (12) T = 25 [µs], f = ( ) [Hz] 205

215 4.,. (1) [g/cm 3 ] = ( ) [kg/m 3 ] (2) [kg/m 3 ] = ( ) [g/cm 3 ] [g/cm 3 ]. 54 [ g ] [cm 3 ] [mm], 100 [mm], 30 [mm] [ g ]., 2.7 [g/cm 3 ] [m], 2 [m], 2 [mm]., 2.7 [g/cm 3 ]. (1) [kg]. (2) [N] [mm], 100 [cm].., 7.9 [g/cm 3 ], π = ,. (1) 4.0 [km/h] = ( ) [m/s] (2) 600 [m/min] = ( ) [km/h] 206

216 [km] 3. (1) [km/h]. (2) [m/s]. (3) 90 [km] 5 [m/s 2 ] [ t ] 5 [m/s], 4, [N]. m v,. m v, f t,. f t, m v = f t [km/h]. [m/s 2 ] [m/min] 5, 18 [m/min]. [m/s 2 ] [m], 1.5 [m], 4 [m]. [Pa]., [kg/m 3 ]. 207

217 [kg] [kpa]. 0.3 [m 2 ]. 16., 1 [m 2 ] [N]. 4 [mm 2 ], [N] , [Pa].,, [cm 2 ]. ( 1 [cm 2 ] [m 2 ].) [N], 12 [m] [W] [kj], 20 [kn] [m] [N], 12 [m] 4. [W] [kw h] [J]. 208

218 5 209

219 1.,. (1) sin θ = (2) cos θ = (3) tan θ = 2.. (1) (2) 3.,. (1) x y. (2). sin θ = cos θ = tan θ = (3) θ. 210

220 4. θ (1) tan 42, tan 35. (2) tan 42, tan 35 x, y. (3) x, y. 211

221 6. A, [m]. A.,. ( ) [m], 35. [m]., 1.6 [m]. 212

222 6 213

223 1. a = (2, 4), b = (3, 1), 3 a 2 b. 2. a = (1, 2), b = (0, 3), 2 a b. 3. a = ( 1, 2), b = (3, 1), 2 a 3 b. 4.. (1) 2 ( a + 3 b ) 3 ( a 2 b ) = (2) 2 ( a 4 b + c ) 2 ( a 2 b + c ) = 214

224 5. a, b, c., d, e, f.,. (1) d = a b c a b c (2) e = a b c (3) f = 2 a + b c 215

225 6., [N]., 3 F = F1 + F 2 + F 3, A(2, 2), B( 1, 0), C(2, 3),. BC, CA, AB 8. 3 A( 2, 2), B(1, 0), C(2, 3),. BC, CA, AB 216

226 9. ABC,. (1) AB AC CB. (2) BC BA. 10. F 1 = F 2 = 10 [N] 2. θ F. (1) θ = 30 (2) θ = 60 (3) θ =

227 11. 30, 1 [N] 45.,. (1) S, N, W,,.. (2) x y. (3) S, N. 218

228 12. 1 [N]. 30, F [N]. S [N],. ( ) (1). (2) F S. 13.,, 30., 30. S [N], T [N],,. W [N]. 219

229 [m], 3.0 [m/s], A, B S 1 S 2, S 3.. ( ) (1) S [m/s]. S 3 [m/s]. (2) A 4.0 [m/s], B. A S 1 θ, tan θ., S 1 [m/s]. (3) S 1 B [ s ]., A B [m]. 15. a = 2 i 2 [m/s]. b, c, d, e, ( )., i, j.,,. (1) b = 5 j (2) c = 2 i 2 j (3) d = 3 i + 3 j (4) e = i j 220

230 7 221

231 1.. (1) 3 2 = 9 (2) 5 2 = 0.04 (3) 2 3 = 8 (4) 2 4 = log a 2 = x, log a 3 = y. x, y. (1) log a (a 6) = (2) log a 128 = (3) log a (9 a 2 8) = (4) log a 36 = (5) log a 3 6 = (6) log a 2 3 a 2 = 222

232 3. x. (1) log x + log(x + 2) 1 2 log 9 = 0 (2) log x 1 = log 2 4. log 2.22 = , log , ( ). 3.9, 2.1.., L 1, L 2 m 1, m 2 m 2 m 1 = 2.5 log L 2 L 1, log 5.3 = [db]., [Pa]., 20 log P [db], P 0 = [Pa]., log 2 = 0.3, P =

233 7.,., log 2 = 0.3, = 5.1.,, [H + ] [OH ]. [H + ] > [OH ], [H + ] < [OH ]., [H + ] [OH ] [H + ][OH ] = (mol/l) 2. (1) (mol/l). ph. (2) ph 2.3. (mol/l). (3), (mol/l). ph. 224

234 8 225

235 1. θ. ( θ, ) (1) 2 sin θ = 0.5, θ =, cos θ =, tan θ = (2) 3 tan θ = , θ =, sin θ =, cos θ = 2.,. (1) sin 70 = (2) tan 230 = (3) cos( 160 ) = (4) sin 570 = 3. [rad],. (1) 45 = (2) π 6 = 4.. (1) 542 (2) 89 5 π 5..,. (1) θ 4 tan θ = 3 3, sin θ, cos θ. (2) θ 2 sin θ = , cos θ, tan θ. 226

236 6..,. (1) θ = 37 [ ], sin θ =, cos θ =, tan θ = (2) θ = 392 [ ], sin θ =, cos θ =, tan θ = (3) θ = 8 π 6 [rad] [ ], sin θ =, cos θ =, tan θ = (4) θ = 13 π 4 [rad] [ ], sin θ =, cos θ =, tan θ = 7..,. (1) sin( 240 ) ( ) 8 (2) tan 3 π 8..,,. (1) θ 3 cos θ = 0.5, sin θ, tan θ. (2) θ 4 sin θ = , cos θ, tan θ. 9..,,. (1) sin 1560 = (2) tan( 680 ) = 227

237 10.. ( ) 23 (1) sin 36 π = ( ) 223 (2) cos 180 π = ( (3) tan 19 ) 90 π = ( 403 (4) cos 180 π ( (5) sin π ( 949 (6) tan 180 π ) = ) = ) = 11. r = 6 [cm]., π. (1) 1 [rad] l. (2) π 3 [rad] l. (3) 2 π 3 [rad] S. (4) r 2 θ [rad] ,, 1 [cm], 2 [cm]. (1), [rad/min]. (2) 12, [cm]. (3) 12, [cm 2 ]. 228