l TRTIONG DHSP TP. HCM KHoA vAr rY Kd'L Hecphan,uil# u* ry Hqc lcj' 2, ndm hgc 2006 - 2007 Lop Cft nh6n vqt lf Thdi gian: 90 phirt OC ttri ft'n 2 Bii 1: Ding kii5n thirc hinh hgc ve dulng vd mflt bQc Z,hdy gi6i thich tqi sao trong thgc t6 nguoi ta ph6ng theo m{t paraboloid trdn xoay dO chiS tpo Sngten thu ph6t s6ng thay vi ph6ng theo c6c m{t cong bdc2 kh6c. Biri 2: he s6 Lame vi thOng sd vi phdn hang nh6t ctia h0 tqa dQ cong ndy. b) Tenxo hiQp bi6n c6 c6c thenh phdn xlz,Ut yz + zx,x+ y+ z trong hQ tga dQ vu6ng g6c. Hdy tim c6c thenh phdn hiQp bii5n cria n6 trong h€ tga ctQ trU. Bni 3: Tinh ma trQn exponent cta ma tr1n a=(o^ ll, , =[o l). r,i r.et ' (o b)' (c o) qua niry suy ra dpi si5 Lie cria nhom Lie ma tran SO(2,R). Biri 4: Dinh nghia mQt dai si5 Lie tr6n trudrng si5 thyc. MO t6 dai sO Lie cria c6c nh6m Lie ma trfln GL(n, R) vd SL(n, R). Ghi chli: - Sinh vi6n khdng tlugc sfr dgng tii li$u . ry Hqc lcj' 2, ndm hgc 20 06 - 20 07 Lop Cft nh6n vqt lf Thdi gian: 90 phirt OC ttri ft'n 2 Bii 1: Ding kii5n thirc hinh hgc ve dulng vd mflt bQc Z,hdy gi6i thich tqi sao trong. trdn xoay dO chiS tpo Sngten thu ph6t s6ng thay vi ph6ng theo c6c m{t cong bdc2 kh6c. Biri 2: he s6 Lame vi thOng sd vi phdn hang nh6t ctia h0 tqa dQ cong ndy. b) Tenxo hiQp. r,i r.et ' (o b)' (c o) qua niry suy ra dpi si5 Lie cria nhom Lie ma tran SO (2, R). Biri 4: Dinh nghia mQt dai si5 Lie tr6n trudrng si5 thyc. MO t6 dai sO Lie cria c6c