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.m²/kg²
- hbar = 1.05457266 x 10^-34 J.s
- c = 2.99792458 x 10⁸ m/s
- k_B = 1.380658 x 10^-23 J/K
using dimensional analysis, construct quantities with the dimensions of:
1. length
2. time
3. velocity
4. mass
5. energy
6. temperature
1. 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?
2. 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?
1. x x^T
2. x^T x
Marion and Thornton 1.2b
1. Marion and Thornton 1.3
2. What is the effect of this rotation on the column vector (2, 1, 5)?
Shankar 8.1.1