Mental Rotation and Imagery
Visual mental imagery has been largely studied within research in perception and cognition. Most people have experienced a "mental image". Try for example, counting the number of windows in your house. Most likely, you form a visual image of each room of your house in order to count the windows.
Mental Rotation of objects is a topic within visual imagery that has been examined by many researchers. Most well-known for this research is Roger Shepard and his colleagues (Shepard and Metzler, 1971; Cooper and Shepard, 1973. They presented pairs of drawings and asked people whether the objects were the same, only rotated, or mirror images of each other.

These studies found, overall, that people took longer to make their judgments as the angular disparity between the two figures increased. In other words, a figure that needed to be rotated 120 degrees to bring it back to the orientation of the first drawing took longer to judge than one needing only 60 degrees of rotation. Thus, judgments were fastest at 0 degree rotation and slowest at 180 degrees.
Furthermore, Cooper and Shepard (1973) found that when advance information about the orientation of the stimulus is given, people could begin mental rotation before the test stimulus appeared. If enough time was given so that people could complete the mental rotation before the stimulus was shown, there was no increase in reaction time with increase in angular disparity.
The finding that people require progressively more time for every additional amount that they must mentally rotate an object, suggests that "mentally rotating" objects is similar to physically rotating objects. The Shepard experiments illustrated the idea that images are internal representations that "stand in" for or "re-present" the corresponding objects.
These studies addressed an intense debate that had begun in the early 1970s about what kind of representation imagery involved. The debate concerned whether mental images were depictive or propositional representations. A propositional representation is a verbal representation or a "mental sentence" that specifies meaning. A depictive representation is a type of picture which specifies the location of objects in space. Results supporting an increase in reaction time to compare objects at increasing orientation suggest that mental imagery is a depictive or analogue representation, similar to the physical object.
Let's look at your data from class. You were asked to decide if pairs of objects (nonsense shapes or letters) were the same or different. The results should look something like the graphs below.

