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## Homework Statement

Suppose

[itex]y = A x [/itex]

where [itex] x,y \in R^2[/itex]

and [itex] A = \left( \begin{array}{cc}

\cos \theta & -\sin \theta\\

\sin \theta & \cos \theta \end{array} \right) [/itex].

Show that y is an anticlockwise rotation of x about the origin.

## Homework Equations

None.

Maybe definition of SO(2,R).

## The Attempt at a Solution

[itex] \square [/itex]

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I kind of don't understand the question.

How can you prove a definition?

Is this question not asking something like, "prove that average speed equals distance over time"?

I guess they want the student to draw a load of triangles? Or perhaps express x and y in terms of polar coordinates to make it more obvious that it's a rotation? Or maybe to show that it can be written as a product of two reflections? Or show that |x| = |y|...but that doesn't make any comments about the angle.

Any suggestions?

Thanks