Final answer:
The map f:E2→E2 given by f(x,y)=(x17y,x2y17) is not an isometry because it does not preserve distances between points.
Step-by-step explanation:
The map f:E2→E2 given by f(x,y)=(x17y,x2y17) is not an isometry because it does not preserve distances between points. An isometry is a transformation of a space that preserves distances, so if two points are a certain distance apart in the original space, they should still be the same distance apart in the transformed space.
To show that f is not an isometry, we can consider two points, say (1,0) and (0,1), and calculate their distance in both the original space and the transformed space. In the original space, the distance between these two points is sqrt(2), but in the transformed space, the distance between f(1,0)=(1,0) and f(0,1)=(0,1) is 0. The distances are not equal, so f is not an isometry.