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

Express ** X** in terms of

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.

Practice the material and concepts discussed in Chapter 1.