Matrix Algebra: Find $v$ for $\|Ax\|_F\leq v \|x\|_F$

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Define real matrix $A_{n \times p}$ and $x_{p \times 1}$. $\| \cdot \|_F$ denote the frobenius norm.

$$\|Ax\|_F \leq v \|x\|_F$$

Can we find a $v$ such that the above inequality holds?