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.
Practice the material and concepts discussed in Chapter 1.