Chapter 5.7, Problem 411E

[T] Find transformations $T_{a,0}:R^2\to R^2,T_{a,0}\left(u,v\right)=\left(u+av+v\right)$ , where $a\ne 0$ is a real number, is called a shear in the x-direction. The transformation , $T_{b,0}:R^2\to R^2,T_{o,b\left(u,v\right)}=\left(u,bu+v\right)$ , where $b\ne 0$ is a real number, is calles a shear in the y-direction a. Find transformation $T_{0,2}\circ T_3,0$

b. Find the images R of the trapezoidal region bounded by u=0,v=0, v=1, and v=2-u through the transformation $T_{0,2}\circ T_3,0$c. Use a CAS to graph the image R in the

d. Find the area of the region R by using region S.