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Interaction Controls
To rotate the coordinate axes around the origin, drag the mouse vertically
over the applet while the The readout at the bottom represents the rotation matrix for the coordinate axes (see below). When you are done with the demonstration, click on the up button at the top of this page, or use your browser's back button to go back to the previous page.
This demonstration is one of a series: you can view the

You can add the squares of the components in each column to see that the length of either coordinate vector remains the same, i.e. equal to one, throughout the rotation.
Also, for those familiar with the dot product, it is possible to check that the two columns of this array, or matrix as it is known, are perpendicular throughout. Any matrix with two perpendicular columns is called an orthogonal matrix.
Once we know the positions of the two axes, we can apply the same rotation to any figure at all. In this case, we rotate a square along with the axes. This is the basis of the rotations that show up in computer animation, and in other applications in twodimensional computer graphics.
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