Homework set # 1. Due: September 8, 12:00 pm (noon).

1.     Find the transformation matrix that rotates a rectangular coordinate system through an angle of 120° about an axis making equal angles with the original three coordinate axes.

 

2.     X is an unknown vector satisfying the following relations involving known vectors A and B and the scalar f:

 

 

 

Express X in terms of A, B, f, and the magnitude of A.

 

3.     Find the value of a needed to make the following transformation orthogonal.

 

 

4.     Show that

 

 

5.     Find the value of the integral

 

 

if the vector A is equal to

 

 

and the surface S is defined by the paraboloid

 

 

where z ≥ 0.

 

Homework set # 1

Practice the material and concepts discussed in Chapter 1.