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.