How to simulate matrix rotations for SVD in R




While reading about SVD I came to know that:
The diagonal matrix:

Geometrically, we may think of a matrix like this as taking a point (x, y) in the plane and transforming it into another point using matrix multiplication:

The effect of this transformation is shown below: the plane is horizontally stretched by a factor of 3, while there is no vertical change.

I wanted to know how do I simulate such a thing in R,it would be good to able to do it myself and understand from there,so if there is any way to do it please do let me know.