Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length 1 if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at (0,0), and that the two equal sides are along the positive x and y axes. Set up the necessary double integrals and use technology to evaluate them.

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