Rotating Cartesian axes

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I have created the following plot in tikz. I was also able to reproduce the same plot with cetz, by using calculations with sin and cos to rotate the axes. I am wondering whether we can use ortho to simplify the code to rotate the axes.

[johannes-wolf]

You can just use rotate(<angle>) to rotate around the z-axis (or any axis if you specify the axis name as named parameter).
Example:

#import "@preview/cetz:0.2.2": canvas, draw
#set page(width: auto, height: auto, margin: .5cm)

#canvas({
  import draw: *

  set-style(mark: (length: .1, width: .2))
  
  line((-2, 0), (2, 0), mark: (end: "barbed"))
  line((0, -2), (0, 2), mark: (end: "barbed"))

  line((0,1), (1,1), (1,0), stroke: (dash: "dashed"))

  line((0,0), (1,1), mark: (end: "barbed"), stroke: red)

  group({
    rotate(30deg)
    stroke(blue)
    line((-2, 0), (2, 0), mark: (end: "barbed"))
    line((0, -2), (0, 2), mark: (end: "barbed"))
  })
})

[psads-git]

What a nice solution! Thanks, @johannes-wolf!