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If `(x , y)` and `(X ,Y)` are the coordinates of the same point referred to two sets of rectangular axes with the same origin and if `u x+v y ,` where `u` and `v` are independent of `x` and `y` , becomes `V X+U Y ,` show that `u^2+v^2=U^2+V^2dot`

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The correct Answer is:
`U^(2)+V^(2)`
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