Why is the copious production of $\Lambda^{0}$ and K particles very difficult to reconcile with their slow decay, without the concept of strangeness? How does strangeness provide a reconciliation?

Find $(a)$ $A^TA$ and $(b)$ $AA^T$. Show that each of these products is symmetric.

$A=$

$$\begin{bmatrix} 0 & -4 & 3 &2 \\ 8 & 4 & 0 &1 \\ -2 & 3 & 5 & 1 \\ 0 & 0 &-3 & 2 \end{bmatrix}$$

Prove that the matrix below is orthogonal for any value of $\theta$.

$$\left[\begin{array}{ccc} {\cos \theta} & {-\sin \theta} & {0} \\ {\sin \theta} & {\cos \theta} & {0} \\ {0} & {0} & {1} \end{array}\right]$$

Use the definition of the derivative to calculate $f^{\prime}.$ $f(t)=t^{2}-\sqrt{t}$

Write inequalities to describe the region. The region between the yz-plane and the vertical plane x = 5

What happens to the $\gamma$ rays that are emitted in stellar nuclear reactions of the proton-proton or carbon cycle?

Sketch the graph of the function. $f(x, y)=10-4 x-5 y$

Data points (x, y) are given. Make semilog and log-log plots of the data.

$$\begin{matrix} \text{x} & \text{5} & \text{10} & \text{15} & \text{20} & \text{25} & \text{30}\\ \text{y} & \text{0.013} & \text{0.046} & \text{0.208} & \text{0.930} & \text{4.131} & \text{18.002}\\ \end{matrix}$$

Find the volume of the described solid $S.$ The base of S is an elliptical region with boundary curve $\(9 x^{2}+4 y^{2}=36\).$ Cross-sections perpendicular to the $\(x-\) axis$ are isosceles right triangles with hypotenuse in the base.

Suppose $a(t)=(15 / 2) \sqrt{t}+3 e^{-t}$, v(0)=-3, and s(0)=4. Find s(t).

a. Use your calculator to approximate $\int_{0}^{b} e^{-0.00001 x} d x$ for b=10, 50, 100, and 1000. b. Based on your answers to part a, does $\int_{0}^{\infty} e^{-0.00001 x} d x$ appear to be convergent or divergent? c. To what value does the integral actually converge?

Assume that each function gives the rate of flow of money in dollars per year over the given period, with continuous compounding at the given annual interest rate. Find the accumulated amount of money flow at the end of the time period. f(t)=1000, 5 years, 6%

Evaluate dw using the given information. $w=x \ln (y z)-y \ln \frac{x}{z} ; \quad x=2, y=1, z=4$, $d x=0.03, d y=0.02, d z=-0.01$

What fundamental law of physics is most responsible for the existence of nuclear magic numbers?