Well, one way to think about what signs are is as directions; positive means pointing right along a number line, and negative means pointing left along that number line.
First off, the convention in the context of Fourier transforms is to think about rotating in the clockwise direction, so let's go ahead and throw a negative sign up into that exponent.
Now, if you want to calculate the magnifying power of the telescope, just start with the same equation you used for the magnifying lens, but with a negative sign, because the image is flipped.
So plus X times the negative expected value of Y. So I'll just say minus X times the expected value of Y. And that negative sign comes from this negative sign right over here.
You have to have that positive mindset that there is always something out there and it is a hard one to have when you have zero dollars and the negative sign in your bank account.
Which means that the induced emf in a coil of wire is equal to the number of coils, times the change in magnetic flux over the change in time, all multiplied by a negative sign.
Geometrically, the meaning of this function is that for any input vector X-Y-Z, you consider the parallelopyped defined by this vector, V and W, then you return its volume with a plus or minus sign, depending on orientation.