Do the following using Matlab : Suppose a model toy set has a spinning disk on it. The disk is centered, in toy world coordinates, at (140, 160) and has a radius of 40 units. It is spinning counterclockwise around its center at a rate of 100 degrees per second. A toy car enters the disk on a road at location (140, 200) heading in the direction (0, 1) and traveling 50 units/second, which will be its speed throughout. The car will continue driving straight ahead, i.e., it does not turn left or right, but as the disk spins the cars orientation will change with the disk until the car travels all the way across the disk and exits the spinning disk.

Write a Matlab script that computes and prints out the cars location in toy world coordinates for each tenth of a second between when the car enters the disk and when it exits the disk. Use geometric transformation matrices from Section 2.7 to solve this problem rather than doing any translation, rotations, scaling, etc. in other ways.

geometric transformation matrices from Section 2.7 :

EXAMPLE 5 Any linear transformation on R2 is represented with respect to homo- TA 01, where A is a 2 x 2 geneous coordinates by a partitioned matrix of the form matrix. Typical examples are T 0 1 0 cos p sin p 0 sin p cos p 0 1 0 0 0 0 1 0 0 1 Scalex by s Counterclockwise Reflection and y by t rotation about the through y EX origin, angle p