a) Find the matrix that represents the linear transformation T :
R3 → R3 that gives a counter-clockwise rotation by the angle θ
about the vector [1, 2, 2]T . Hint: To rotate a vector v, first
orthogonally project v onto a plane normal to [1, 2, 2]T to
obtain the vector w. Then rotate w about the axis by taking a
suitable linear combination of w and a vector in the plane
normal to w having the same length as w. Then add the
appropriate vector to find the image of v under the rotation. b)
A box has its edges parallel to the coordinate axes with a pair
of opposite vertices having coordinates (2, 0, 0) and (4, 1, 1).
Use Excel to compute the coordinates of the eight vertices of
the box under the above transformation using θ = π/3 and θ =
2π/3. c) We wish to use Excel to plot the original box along
with its two rotated images. To do so find a linear
transformation S : R3 → R2 whose input is a point [x,y,z]T in R3
and whose output is the coordinates of the representation of
that point (as it would be plotted in a t