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A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\BbbR^2\to\Bbb R^2$ given by two polynomials of two variables. Such atransformation is called quadratic if the degrees of its polynomials are notgreater than two. In the present paper an exhaustive description of invertiblequadratic transformations of the real plane is given. Their application to theperfect cuboid problem is discussed.

A note on invertible quadratic transformations of the real plane