Homework #2
Read Marion and Thornton Chapter 1, Shankar Chapter 7, 8.
 Use MKS units throughout and give the answers both analytically and
numerically. From the following four fundamental constants (and only these)
 G = 6.67259 x 10^{11} N.m^{2}/kg^{2}
 hbar = 1.05457266 x 10^{34} J.s
 c = 2.99792458 x 10^{8} m/s
 k_{B} = 1.380658 x 10^{23} J/K
using dimensional analysis, construct quantities with the dimensions of:
 length
 time
 velocity
 mass
 energy
 temperature

 In the matrix equation D = ABC, if D is a 2x2 matrix, A is a 2x5 matrix,
and C is a 2x2 matrix, what are the dimensions of B? How many rows and
how many columns?
 Write the matrix equation D=ABC in index notation. Include limits on
the sums.
 If x is the column vector with components (1,2,3), what is the result of
the following matrix multiplications?
 x x^{T}
 x^{T} x
 Marion and Thornton 1.2b

 Marion and Thornton 1.3
 What is the effect of this rotation on the column vector (2, 1, 5)?
 Shankar 8.1.1