Given that $a$ is a negative odd number, let's determine the properties of $a^2$.

1. Sign: When you square any number, whether it's negative or positive, the result is always positive. Therefore, $a^2$ is positive.

2. Parity: Squaring an odd number results in another odd number. So, $a^2$ is odd.

Thus, the two words that describe $a^2$ are positive and odd.

Would you like further details or have any other questions?

Here are five related questions to consider:

1. What happens when you square a negative even number?
2. How does the square of an even number differ from the square of an odd number?
3. If $a$ was positive and even, what would be the properties of $a^2$?
4. Can a square of any integer ever be negative?
5. What is the effect of squaring a fraction compared to squaring an integer?

Tip: Remember, squaring a number always results in a positive value, regardless of whether the original number is positive or negative.