Final answer:
The magnitude of vector a with components 9 and -5 (assuming the negative magnitude was a typo) is calculated using the Pythagorean theorem as \(\sqrt{106}\) or \(\sqrt{2 \times 53}\), which is in simplest surd form.
Step-by-step explanation:
The question asks to find the magnitude of vector a given the components of the vector. The magnitude of a vector is found using the Pythagorean theorem based on its components. If the given vector a has components Ax = 9 and Ay = -5, then the magnitude is calculated as |a| = \(\sqrt{9^2 + (-5)^2}\). However, magnitudes of vectors are always non-negative, so the negative sign given in the question seems to be an error. Assuming this is a mistake, and interpreting the magnitude as |a| = \(\sqrt{9^2 + 5^2}\), it simplifies to |a| = \(\sqrt{81 + 25}\) = \(\sqrt{106}\) = \(\sqrt{2 \times 53}\), which is the simplest surd form.