How to prove some functions are scalar field or vector field

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Homework Statement


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Homework Equations

The Attempt at a Solution


I solved #2,4 but I don't understand what #1,3 need to me. I know that scalar field is a function of points associating scalar value. But how can I prove some function is scalar field or vector field?
 
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That's a good question. What does your textbook say?
 
Text says scalar is invariant in rotational transformation.Then to prove some functions are scalar field, should I do rotational transformation, or are there any other methods?
 

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