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h1. Scalar

{excerpt}A quantity that does not have a direction associated with it.{excerpt}

h3. Negative Scalars

It is important to note that some scalar quantities can be negative.  For instance, money is a scalar.  You cannot earn "$5 east" or "$5 at 60° south of west".  You can, however, owe someone money.  Suppose you are a student with $10,000 in loans and no appreciable assets.  You might then say your net worth is -- $10,000.  The negative sign attached to a scalar functions very differently than the negative sign of a one-dimensional vector.  When comparing vectors, we usually compare magnitudes.  Thus, a velocity of 50 m/s *west* might be denoted as -- 50 m/s, but it is still larger than a velocity of 20 m/s *east*.  A net worth of -- $10,000 is certainly _*not*_ larger than a net worth of $5,000!

Some examples of scalars that are constrained to be positive are:
* [mass]
* [distance]
* [kinetic energy]
* thermal energy

Some examples of scalars that can be negative are:
* [work]
* [potential energy]
* [mechanical energy]

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