Example 1.9 shows how to represent rotation of all vectors in the plane through an angle θ about the origin, with respect to the standard bases.
(a) Rotation of all vectors in three-space through an angle θ about the x-axis is a transformation of R3. Represent it with respect to the standard bases. Arrange the rotation so that to someone whose feet are at the origin and whose head is at (1, 0, 0), the movement appears clockwise.
(b) Repeat the prior item, only rotate about the y-axis instead. (Put the person's head at 2.)
(c) Repeat, about the z-axis.
(d) Extend the prior item to R4.