Yup. Whenever you convert units to a power, both sides of the convertion must be to the same power.
The answer should end up being aroung 16.8 IIRC, converting CC to cu. in. (I'm a car fanatic, and do these calculations often when figuring muscle car engines)
One area of physics where the cross product is used a lot is rotational forces, such as torque and centrifugal force.
So, think of a rotating cylinder. Now picture your hand representing the forces of that cylinder.
With your hand uncurled, the tips of your fingers point raially outward...
For the first question, an answer of it isn't differentiable because its not continuous seems to be the answer that would be appropriate to me.
2nd question, yes, it should be differentiable at f'(1). Because the slopes (derivatives) are the same at point x = 1, then it shouldn't have a...
Think of it like a triangle.
Since the pilot wishes to fly due west, it must counteract the south wind with the Y component of the plane's velocity due north of equal magnitude. So one leg of the triangle is 88 mph north, or posotive Y if its easier to think that way.