1. Calculate the deformation gradients for the following operations. As discussed in class,
(X,Y,Z) correspond to the original configuration and (x,y,z) correspond to the new,
updated configuration (5 points each).
a. $x = 2X\cos\theta + 3X\sin\theta$; $y = 3Y + 2X\sin\theta$
b. $x = 2X + 5Y$; $y = 3X + Y\cos\theta$