No
The answer is simplest form
A conversion factor is the same as multiplying by a factor of?
10
Similar objects. "Same shape" is not exactly well-defined, but I think if they are "proportional" to each other (where taking one and multiplying *all* dimensions by a scalar yields the other), they are "isomorphic."
#
If you intend 'dimensions' to mean units then whenever the two quantities are to be operated on each other then they must have the 'dimensions', refer to dimensional analysis
Yes.
Yes they must be in the same units of measurements.
No, it is not true.
The answer is simplest form
Efficiency is a ratio of the same quantities. Usually, output power / input power. As the numerator and denominator have the same quantities, the dimensions cancel each other out.
Squaring for multiplying, and if you are dividing by the same number, you get 1
There is no particular name for it. For example, the frequency and wavelength of electromagnetic rays are related, but multiplying them by the same number, or dividing, makes no sense.
if they have same units they must have same dimensions . but thy can have different units even if they have same dimensions i hope it helps :
They must have the same dimensions.
When two physical quantities are added together, they must have the same units in order to be combined. This means that both quantities must be expressed in the same type of measurement, such as meters or kilograms, for the addition to be valid.
The matrices must have the same dimensions.