Effect of transformation on a point.

Question

What is the effect of the transformation $$A(x,y)=(0.6x-0.8y, 0.8x+0.6y)\quad ?$$

I understand how transformations work when the variables are not in the same coordinate. I do not understand how I could predict the effect.

Answer 1

The matrix for this transformation is $$ \begin{pmatrix} 0.6&-0.8\\ 0.8&0.6 \end{pmatrix} $$ This is an example of rotations.

The effect of your transformation is rotating a point around the origin by an angle $\theta$ where $\cos\theta=0.6$.