# ScalingX/Y-RotationX/Y Method

The first method involves specifying the individual x- and y-scaling and x- and y-rotation values of the 2D linear transformation. Each value can vary independently of the others.

If you decompose the general 2D linear transformation’s (2x2) matrix into two (2x2) matrices, the first of which represents the x- and y-rotation and the second represents the x- and y-scaling, you get the following:

where:

- Sx is the x-axis scaling.
- Sy is the y-axis scaling.
- θx is the x-axis rotation.
- θy is the y-axis rotation.
- Tx and Ty are the x- and y-translation.