# Matrix transform

Source: http://www.xkcd.com/184/

P.S. In case you don’t get the joke… and are wondering why the answer isn’t $[a_2, -a_1]^T$…  the matrix is an example of a rotation matrix. This concept appears quite frequently in linear algebra (not to mention video games and computer graphics). In the secondary mathematics curriculum, this device is often used to determine how to graph conic sections of the form

$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$,

where $B \ne 0$. I’ll refer to the MathWorld and Wikipedia pages for more information.