IN MATHEMATICA:

Consider a transformation "T" that takes and takes a point in R2 and rotates it some angle "t" counterclockwise.

a. Define a matrix A that performs the transformation.

b. Define a point to be {1,2}. Multiply the point by your Matrix using a value of "t" that yields a rotation of 45 degrees. Plot both the point {1,2} and the new rotated point on a graph.

c. Create a manipulate with parameter "t" that models the rotation caused by the transformation.

How do you do this in Mathematica?