```
Clear["Global`*"];
a = .3*2 π;
η = x*Cos[a] + y*Sin[a];
ζ = -x*Sin[a] + y*Cos[a];
g = 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];
{g, g /. {x_Real, y_Real} :> {Sqrt[x], Sqrt[y]}}
```

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

* or 

```
a = .3*2 π;
Show[ContourPlot[
  x*Cos[a] + y*Sin[a] /. {x -> x^2, y -> y^2} // Evaluate, {x, 0, 
   10}, {y, 0, 10}, Contours -> {1, 2, 3}, ContourShading -> None], 
 ContourPlot[-x*Sin[a] + y*Cos[a] /. {x -> x^2, y -> y^2} // 
   Evaluate, {x, 0, 10}, {y, 0, 10}, 
  Contours -> {-3, -2, -1, 0, 1, 2, 3}, ContourShading -> None]]
```

  [1]: https://i.sstatic.net/UmqbDNQE.png
  [2]: https://i.sstatic.net/lQnIhRG9.png