Note: Click-drag to measure coordinates. The moving frame uses the blue coordinates. The lab frame uses the gray coordinates.
Coordinate transformations are ubiquitous in physics. Every freshman physics student quickly learns that it is easier to solve a block on an incline plane if the x and y axis are chosen to lie parallel and perpendicular to the incline. A rotation of spatial coordinates doesn't change the physics but it makes the math necessary to do the problem simpler.
The Lorentz transformation shown above is the coordinate transformation predicted by Einstein's Special Theory of Relativity. The horizontal axis is measures the x position of an event and the vertical axis measures the time if an event. The blue coordinate lines show how events in a stationary frame transformation when viewed from a moving frame. You can use this applet to study how the position and the time coordinates depend on the relative velocity of these two frames.
Although the Minkowski Physlet was designed to show the Lorentz transformation, it can also be used to show simple rotations and the classical Galilean transformation.