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In Exercises 5-7, find positive numbers $a$ and $b$ so that the change of coordinates $s=ax,t=by$ transforms the integral $∬_{R}dxdy$ into $∬_{T}∣∣ ∂(s,t)∂(x,y) ∣∣ dsdt$ for the given regions $R$ and $T$.
7. $R$ is the rectangle $0≤x≤50,0≤y≤10$ and $T$ is the square $0≤s,t≤1$.

Let us consider the given problem:

Now, we are to find the positive numbers and so that change of coordinates transforms the given integrals in the desired form.

Given the rectangle is such that and , and the square is such that .

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