Formaldehyde (HCHO) has no alkyl group to donate electrons, so the carbonyl carbon is most electrophilic (least steric hindrance, smallest +I effect).

$\frac{I_{max}}{I_{min}} = \left( \frac{a_1 + a_2}{a_1 - a_2} \right)^2 = 16 \implies \frac{a_1 + a_2}{a_1 - a_2} = 4$.

$a_1 + a_2 = 4a_1 - 4a_2 \implies 5a_2 = 3a_1 \implies \frac{a_1}{a_2} = \frac{5}{3}$.

Intensity ratio $\frac{I_1}{I_2} = \left( \frac{a_1}{a_2} \right)^2 = \frac{25}{9}$.

Organizations are flattening (reducing management levels between CEO and production workers) in an effort to become more competitive. The traditional middle management role has been equated with cumbersome bureaucracy that prevents businesses from responding to market forces.

Oxidative phosphorylation occurs in the inner mitochondrial membrane (or bacterial plasma membrane) via the electron transport chain and ATP synthase. It couples chemiosmosis with ATP synthesis.

$A = \begin{pmatrix}i&-i\\-i&i\end{pmatrix}$. Note $\det(A) = i^2-i^2=0$, so $A$ is singular.

$A^2$: compute $(A)^2$. Row1·Col1: $i(i)+(-i)(-i)=-1+(-1)=-2i$... Let's compute: $A^2_{11}=i\cdot i+(-i)(-i)=i^2+i^2=-1-1=-2$. So $A^2 = -2A$... check: $A^2 = -2\begin{pmatrix}i&-i\\-i&i\end{pmatrix}$.

Therefore $A^8 = (-2)^4 A^4 = 16(A^2)^2=16\cdot4A^2=64\cdot(-2A)=-128A$.

Wait: $A^2=-2A \Rightarrow A^4=4A^2=-8A \Rightarrow A^8=-8A^4... $ Correctly: $A^8=(-2)^7A = -128A$.

$-128A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}8\\64\end{pmatrix}$. Since $\det(A)=0$, check consistency. The equations are linearly dependent but RHS $(8,64)$ is not in column space of $A$. Hence no solution.