An Interactive Applet powered by Sage and MathJax.
(By Prof. Jane Long, based on an activity of Prof. Tom Judson, with some tiny modifications by Prof. Gregory Bard. Updated by Ryan G. Hornberger.)
This is perhaps one of the most famous Sage Interacts/Applets of all time.
To understand the graphical aspects of matrix transformations, we can choose any matrix that we like, and the applet will show us what happens to the smiley face.