1. **State the problem:** We are given the formula $$F = 1 - \left(\frac{M}{K}\right)^2$$ and need to transpose it to make $M$ the subject. 2. **Isolate the squared term:** Start by moving terms to isolate $$\left(\frac{M}{K}\right)^2$$. $$F = 1 - \left(\frac{M}{K}\right)^2$$ Subtract $F$ from both sides: $$1 - F = \left(\frac{M}{K}\right)^2$$ 3. **Take the square root:** To solve for $\frac{M}{K}$, take the square root of both sides: $$\sqrt{1 - F} = \sqrt{\left(\frac{M}{K}\right)^2}$$ $$\sqrt{1 - F} = \left|\frac{M}{K}\right|$$ 4. **Remove the absolute value:** Since $M$ can be positive or negative, $$\frac{M}{K} = \pm \sqrt{1 - F}$$ 5. **Solve for $M$:** Multiply both sides by $K$: $$M = \pm K \sqrt{1 - F}$$ 6. **Summary:** The subject $M$ is: $$\boxed{M = \pm K \sqrt{1 - F}}$$ This means $M$ equals plus or minus $K$ times the square root of $1 - F$.