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In Acute Myocardial Infarction (AMI), the priority nursing assessment is continuous cardiac monitoring and 12-lead ECG because:
- AMI causes life-threatening arrhythmias (ventricular fibrillation, ventricular tachycardia) in the first hours
- ECG identifies the infarct location, extent, and guides reperfusion decisions
- Time-to-treatment (door-to-balloon time ≤ 90 minutes for STEMI) is the key determinant of outcomes
The 4 Ts of AMI nursing priority:
- Time (ECG within 10 minutes)
- Thrombolytics/PCI preparation
- Therapy (MONA: Morphine, Oxygen, Nitrates, Aspirin)
- Telemetry (continuous cardiac monitoring)
Cardiac biomarkers (Troponin I/T) are diagnostic but take time. ECG provides immediate actionable information.
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 $= \mathbf{4}$
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