Use Chargaff's rule to determine the percentages of complementary base pairs. If adenine is 30%, thymine will also be 30%, and the remaining 40\% is split equally between cytosine and guanine.
In double-stranded DNA, the base pairing rule states that adenine (A) pairs with thymine (T), and cytosine (C) pairs with guanine (G). According to Chargaff's rule, the percentage of adenine equals the percentage of thymine, and the percentage of cytosine equals the percentage of guanine. Given that the DNA contains 30% adenine, it must also contain 30% thymine. This leaves 40% of the DNA to be divided equally between cytosine and guanine, resulting in 20% cytosine and 20% guanine.
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]