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."
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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.
Yes, two quantities must have the same dimensions if they are to be equated. This is because equations represent a balance or equality between the two quantities, and quantities with different dimensions cannot be compared or equated meaningfully. For example, equating speed (meters per second) to time (seconds) is invalid as they have different dimensions.
Yes, two quantities must have the same dimension in order to be added together. This is because addition involves combining like terms, and only quantities with the same dimensional units can be meaningfully combined. For example, you cannot add meters and seconds, as they represent different dimensions.
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.
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.
Squaring for multiplying, and if you are dividing by the same number, you get 1
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.