A certain point has rectangular coordinates $(10,3)$ and polar coordinates $(r, \theta).$  What are the rectangular coordinates of the point with polar coordinates $(r^2, 2 \theta)$?
Question:
A certain point has rectangular coordinates $(10,3)$ and polar coordinates $(r, \theta).$  What are the rectangular coordinates of the point with polar coordinates $(r^2, 2 \theta)$?
Answer:
Let's think step by step.

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A certain point has rectangular coordinates $(10,3)$ and polar coordinates $(r, \theta).$  What are the rectangular coordinates of the point with polar coordinates $(r^2, 2 \theta)$?
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