Clear["Global`*"];
a = .3*2 π;
η = x*Cos[a] + y*Sin[a];
ζ = -x*Sin[a] + y*Cos[a];
Show[ContourPlot[η, {x, 0, 10}, {y, 0, 10},
Contours -> {1, 2, 3}, ContourShading -> None],
ContourPlot[ζ, {x, 0, 10}, {y, 0, 10},
Contours -> Range[-3, 3], ContourShading -> None],
PlotRange -> All,
AspectRatio -> Automatic] /. {x_Real, y_Real} :> {Sqrt[x], Sqrt[y]}
- or maybe
/. {x_Real, y_Real} :> {x^2, y^2}