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4. 0 + 0 0 0 0 3. 0 + 0, 0 + + 4. + 0 ( + + (3 3 0 + 3 Ke Words: 4. A e, e, v, v 0 e, e 0, v, v e, e v, v B e + e v, v
5 5. A,, B a, b, c + + ( ( + a + b + c + 6. A 0 ( + + ( + z + (z + 0 0 B ω ω 3 a, b, c z + a z + b c ω z ω 7. A v v 0 B (,, 0, (, 0,, (0,, H (, a, b H 3. (, 0 θ cos θ 0 sin θ R θ 0 cos θ sin θ
6. π 360 π (0, θ 0 R θ sin θ cos θ. (, R θ (c v + c v c R θ (v + c R θ (v R θ (v + v R θ (v + R θ (v, R θ (cv cr θ (v R n v n R n T (v R n 3 T : R n R n v T (v 5. id id(v v 3 T v v
6. c 7 D c (v cv R n c D id 7. a R n T a (v v + a R n a 0 T 0 id R n R R n T T (c v + c v c T (v + c T (v T (v + v T (v + T (v, T (cv ct (v ( 0 R θ R θ + 0 0 R θ + R 0 θ cos θ sin θ + sin θ cos θ cos θ sin θ sin θ + cos θ 0 + v 0 v ( θ cos θ sin θ R θ (v sin θ cos θ (, z + i
8 θ w cos θ + i sin θ z + i z wz + i (, θ (, R θ wz wz (cos θ + i sin θ( + i ( cos θ sin θ + i( sin θ + cos θ θ cos θ sin θ R θ sin θ + cos θ T w cos θ + i sin θ T (z wz v, v z, z c v + c v c z + c z T (c z + c z w(c z + c z c wz + c wz c T (z + c T (z T Ke Words: 8. ( 3/, / π/3 9. (, (, π/4 0. v v +. v w θ (v, w + (v, w v w cos θ
9. A θ l l S θ 0 S θ, S 0 θ B S θ S θ S θ cos θ + sin θ sin θ cos θ 3. 4 d d f(, g( c, c d ( d c f( + c g( c d d f( + c d d g( d n d n ( n n! ( ( n+ ( + n+ 4. A a, b, c f( f(a, f(b 0, f(c 0 B a f( a f( a f( a f(a f(, g( c, c ( cf( + cg( c f( + c (g( a a a f( f( p, f( q, f(3 r 4. R n (0,..., 0 T 0. 0 4 f( + g( c f( d d
0 0 0+0 0 T (0+T (0 T (0 T (0 T (0 0. R n T R n R n l v, 0 w l {v + tw R n t R} t v + tw R n T T (l {T u u l} l T T l T (l u v + tw T (u T (v + tt (w T (w T (l T v R R T R T ( c R T : R R T ( T ( T ( c c T c R c R R n Ke Words: R n 5. R 6. a T a (v v + a 7. (, ( +,
5. θ cos θ sin θ sin θ + cos θ a b 4 a, b, c, d c d a, b, c, d ( a b ( c d a c b a (, d (, ( b(, c(, d a b M v Mv c d a b a + b Mv c d c + d Mv M, a b Mv + c d cos θ sin θ R θ (, sin θ cos θ cos θ sin θ R θ sin θ cos θ cos θ sin θ θ sin θ cos θ ( R T T T
T ( 0 T + 0 0 T + T 0 T 0 T T a, T c a + c b d 0 a b c d b d a b c d T ( a b a b a b α + β α + β c d c d c d a b. T c d R 4 a b T, c d ( 0 a b T, T 0 c d 8. R id E 0 0 v Ev v
9. T T 3 a, T c b d T T ( T T + 0 T + T a + b, c + d ( 0 T T T T a b c d a + b a b T c + d c d 3 + + T T + a + c b d a + b a b c + d c d 0. D c R θ S θ c θ t Z AFTER BEFORE X P Q t t.5 t C t 0.5 t t0 S R t0.5 A B t t.5 D C t Y Figure.
4 C t v t v t t C t BEFORE AFTER t 0 D ABCD PQRS t 0 C t t ± XY SZ R Ke Words: 8. 9. R T T a, T b c d T 0. A 3 A v B t λ(t ( t t Av + v λ(tv v λ(t λ(t v t. A R T T + 3
T B R T 0 3 T, T 0 T 5. A π/3 B R P (, 0 π/3 (, P 3. (, (, (, (, 4. + (, 6. θ θ v v R θ (v v R θ (v R θ (R θ (v v v R θ R θ R θ R θ R θ R θ R θ +θ ai b A i i (i, T i T T c i d i ( a b a b T T T + T c d + T c d a a a T T A + b c b A c c a + d c d a b + b d A c b + d d A A A a b a b a a + b c a b + b d c d c d c a + d c c b + d d R θ R θ R θ R θ R θ +θ
6 S θ (cos θ sin θ cos θ sin θ cos (θ θ sin (θ θ sin θ cos θ sin θ cos θ sin (θ θ cos (θ θ S θ S θ R (θ θ S θ S θ R (θ θ (, ( +, T (, (, + T + ( + + T T T + + + T T (, ( +, + T T + + + T T T ( + + + (, ( +, + T, T 0 T, T 0 0 T T 0, T T ( 0 0 A, B A B Ke Words: 5. X, Y X, Y 3 XY Y X 3 6. A R θ R θ R θ +θ
7 B R θ S 0 S θ 7. A θ l θ (r, ϕ l θ B l, l P l i (i, S i P θ l l S S P θ P 7. m n m n m n m n m n (m, n (i, j A (a ij i,...,m j,...,n A (a ij i,j,...,n n a a a n a a a n A... a m a m a mn m (i, j i a a j a n a a a n... a ij... a m a m a mn. ( i + j i, j,,3 ( 3 3 4 4 5 (m, n A + B (a ij i,...,m j,...,n ca c(a ij i,...,m j,...,n + (b ij i,...,m j,...,n (ca ij i,...,m j,...,n (a ij + b ij i,...,m, j,...,n
8 (l, m A (m, n B C AB m c ij a ik b kj a i b j + a i b j + + a im b mj k AB (a ik i,...,l (b kj k,...,m k,...,m j,...,n AB (l, n 00 k k + + + 99 + 00 5050, ( m a ik b kj j i,...,l j,...,n m j 00 k k + + + 99 + 00 338350. A, B A B AB 3 3 + 5 4 Figure. 3 3 A B AB 7 5 3 4 57 79 56 55 97 m v n t w v t w m n t wv m n
3. v, t w ( 3 v t w 9 ( 3 6, t wv 5 m n m n m n Ke Words: m n 8. 9. 0 3 0 4 0 3 3 0 4 0 3 + + z + z + + z 30. A,B /3 A, B 0 /3 0 AA, AB, BA, BB 3. A X, Y, Z X ( i j i0,,, Y ( i j j0,, Z ( j i i0,, j0, i0,, j0, B A, B, C A ( i j i0,...,l, B (z j w k j0,...,m, C ( i w k i0,...,l j0,...,m k0,...,n k0,...,n AB (/zm /z C
0 8. A, B, C c (ABC A(BC, A ( ( 0, B 0 ( ( 0 (ABC 0 A(B + C AB + AC, (A + BC AC + BC, (cab A(cB c(ab, C ( ( ( A(BC ( ( (0 ( 0 A ( 0, B, C 0 A(B + C ( ( 0 + ( ( 4 5 0 AB + AC ( + ( 0 ( 3 + ( 3 ( 4 5 0 c 5, A ( 0, B 0 (cab ( 5 ( 0 ( 5 5 0 ( 5 5 0 0 A(cB ( ( 0 5 ( 0 5 ( 5 5 0 5 0 ( ( 0 c(ab 5 5 ( ( 5 5 0
a ij b jk c kl a ij b jk c kl k j j k a ij b jk c kl a ij b jk c kl j k j k X jk j j k X jk k n A A k (k N k 0 A 0 E, A k+ AA k E n AE A, EB B 0 O AO O OB O O Ke Words: 3. 3 3 M a b c M a b c ( a b c za zb zc z
g ( a b c a + b + cz z M 00 33. A α, β M(α, β αe + βa M(α, β M(γ, δ B A, A, A 3 0 0 0 A, A 0, A 0 3 0 N(α, β αa + βa N(α, βn(γ, δ N(γ, δn(α, β (αδ βγa 3 34. A A, B A (, B (, A A, B B, AB BA O, A + B E B 3A + B n + 3 n 3 n 3 n + 3 n 35. M 3 N 3 MN
3 9. R n T S T T S S T id v T T v Sw S w R n 4. D c D c T a T a R R θ R θ R S θ n A B AB BA E B A A B B A B BE B(AB (BAB EB B B B A A A n A (a ij i,j,...,n i j a ij 0 A 0 0 a ii 0 n (b jk j,k,...,n (AB ii n a ik b kj a ii b ii 0 k AB E
4 k N k O N N E N E + N + N +... + N k (E N(E + N + N + + N k (E + N + N + + N k (N + N + + N k E N k E n A (a ij i,j,...,n i > j a ij 0 A 5. 3 0 0 0 0 0 0 0 0 3 N 0 n 4 0 0 0 0 0 0 0 0 0 0 N 0 0 0 0 0, N 0 0 0 0 0 0 0, N 3 0 0 0 0 0 0 0 0, N 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 N 3. X E + X + X + X X E X n A, B B A AB (B A (AB E (AB (B A A(BB A AEA AA 3. A (a i,j i,j,...,n 0 i a i,i 0 i a i,i 0 A D N E D A N n 0 A D(E N
i n 5 { 0 j < i a jj 0 j i n v Av 0 A 0 A 0 A Av Ev v A A B b C A 0 0 C O 0 C 3 B (i (i b (i B b v 0 Av 0 6. 0 0 0 0 0 0 + 0 0 0 0 0 0 0 0 0 0 0 + 0 0 0 0 0 0 0 0 0 0 0 0 : Ke Words: 36. 0 A 0 0 0 37. A A, B a 0 0 0 A 0 b, B a 0 0 0 0 b
6 B + a a 0 AB a + b b 0 b 38. N 4 ( 0 + ( 4 + + 8 4 0 0 0. a b (. A A ad bc c d 4. a b A c d 0 A ad bc 0 A d b ad bc c a d b à c a a b d b ad + b( c a( b + ba Aà (ad bce c d c a cd + d( c c( b + da ÃA (ad bce A ad bc 0 A d b ad bcã ad bc c a
7 A A 0 AÃ O A AÃ O A AÃ O Ã O A O E A A O A. A. A u, w A u t w A ( A 0 a b A ad bc 0 c d 0 (c (a, b (0, 0 A d (a a 0 d bc/a A b c/a (a b 0 c ad/b A b d/b A v 0 Av 0 {Av v R } R v A(v A
8 A O A O A u t w (u, t w 0 (i 0 t w n 0 0 n t w ( 3 3 n An (u t wn u ( t w n 0 n (ii v R t w v Av (u t wv u ( t w v ( t w vu Av {tu t R} A 3 n An v Av { t t R} 3 6 ( 3 3 0 ( ( 3 ( 3 ( + 3 7. r s + r, + 4 s
A, v 4 Av b 9, b r, s 4 A v A b 4r s r + s, 0 r, s A b a b r A, b c d s Av b A b A Av b v A b O b 0 v A u t w u w b {tu t R} b su, t wn 0 n t wa a {sa + tn t R} Ke Words:
30 39. A p, q, r, s A p (i A 0, q (ii v Av B { t r t R} s 40. A R T B R l (a, b (0, 0 a, b, c R a + b c T l R C T l 4. α, β A A α, A β 4. (, 3 6 s 3 s