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The Hays Code (officially the Motion Picture Production Code) was:
- Named after Will H. Hays, who headed the Motion Picture Producers and Distributors of America, established in 1922 after Hollywood scandals
- Formally promulgated in 1934 and complied with by virtually every Hollywood producer
- It imposed highly restrictive guidelines on depictions of sexuality, violence, crime, religion, and language
- Abandoned in 1966, replaced by the Motion Picture Code and Rating Program with four initial ratings: G (general audiences), M (mature, parental guidance), R (restricted, no under-18 without parent), and X (no under-18)
- Later, M was replaced by PG (parental guidance), PG-13 was added, and NC-17 replaced X
The Hays Code represented a system of industry self-censorship designed to avoid government-imposed censorship โ an attempt to make the Social Responsibility Theory function through voluntary compliance rather than regulation.
Count the total number of $3\times3$ matrices of the form $A=\begin{pmatrix}0&2y&1\\2x&y&-1\\2x&-y&1\end{pmatrix}$ with $x,y\in\mathbb{R},\ x\neq y$, satisfying $A^TA=3I_3$.
Compute $A^TA = 3I_3$ by equating columns to be orthogonal with magnitude $\sqrt{3}$.
Column 1 norm$^2$: $0+(2x)^2+(2x)^2=8x^2=3 \Rightarrow x^2=\frac{3}{8}$: 2 values of $x$.
Column 2 norm$^2$: $4y^2+y^2+y^2=6y^2=3 \Rightarrow y^2=\frac{1}{2}$: 2 values of $y$.
With $x\neq y$: we need to discard cases where $x=y$. Since $x^2=3/8$ and $y^2=1/2$, $x\neq\pm y$ (different magnitudes), so all $2\times2=4$ combinations are valid.
Total $= \mathbf{4}$
Evaluate: $\displaystyle\lim_{x\to0}\dfrac{x\cot(4x)}{\sin^2 x\cdot\cot^2(2x)}$
Rewrite using $\cot\theta = \cos\theta/\sin\theta$:
$\dfrac{x\cdot\cos4x/\sin4x}{\sin^2x\cdot\cos^22x/\sin^22x}$
As $x\to0$: $\sin4x\approx4x$, $\sin2x\approx2x$, $\sin x\approx x$, all cosines $\to1$:
$\approx\dfrac{x\cdot\frac{1}{4x}}{x^2\cdot\frac{1}{4x^2}} = \dfrac{\frac{1}{4}}{\frac{1}{4}} = \mathbf{1}$
The basic management functions that all managers perform include:
The text states that basic functions all managers perform are planning, organizing, staffing, leading, and controlling. HR management specifically involves policies and practices for the staffing (people) function within this framework.
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