```
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]}
```
[![enter image description here][1]][1]

* or maybe `/. {x_Real, y_Real} :> {x^2, y^2}`


  [1]: https://i.sstatic.net/7Z5wnReK.png