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(B) To eliminate the $xy$ term in a general quadratic equation $ax^2 + bxy + cy^2 + dx + ey + f = 0$,the axes must be rotated by an angle $	heta$ suc

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$	heta_3, 	heta_1, 	heta_2$

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(B) To eliminate the $xy$ term in a general quadratic equation $ax^2 + bxy + cy^2 + dx + ey + f = 0$,the axes must be rotated by an angle $	heta$ such that $	an 2	heta = \frac{b}{a-c}$.For $A_1$: $a=3, b=5, c=3$. $	an 2	heta_1 = \frac{5}{3-3} = \infty$ $\Rightarrow 2	heta_1 = \frac{\pi}{2}$ $\Rightarrow 	heta_1 = \frac{\pi}{4}$.For $A_2$: $a=5, b=2\sqrt{3}, c=3$. $	an 2	heta_2 = \frac{2\sqrt{3}}{5-3} = \sqrt{3}$ $\Rightarrow 2	heta_2 = \frac{\pi}{3}$ $\Rightarrow 	heta_2 = \frac{\pi}{6}$.For $A_3$: $a=4, b=\sqrt{3}, c=5$. $	an 2	heta_3 = \frac{\sqrt{3}}{4-5} = -\sqrt{3}$ $\Rightarrow 2	heta_3 = \frac{2\pi}{3}$ $\Rightarrow 	heta_3 = \frac{\pi}{3}$.Comparing the angles: $\frac{\pi}{3} > \frac{\pi}{4} > \frac{\pi}{6}$,which means $	heta_3 > 	heta_1 > 	heta_2$.

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