A remotely-operated vehicle is sent to the deepest part of the Mariana Trench. It returns with a sample of rock from the ocean floor. Would this rock be old or young? Explain.

Give an example of how changes in the cryosphere affect the biosphere.

A northern right whale migrates from warm waters off Florida to cooler waters off Nova Scotia, Canada. In which area do you think more thermal energy would move from the whale to its environment? Explain.

Give an example of the hydrosphere interacting with the geosphere.

The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at the ocean floor is huge, about $1.13 \times 10^8$ N/m$^2$. Explain whether or when it is a good approximation to think of water as incompressible.

Describe the hypothesis of continental drift.

Suppose Bob creates two RSA encryption algorithms as follows: First, he picks large primes p and q and calculates $n$=pq. Next he choose two integers $e_1$ and $e_2$ with $\gcd(e_1,\varphi(n))=\gcd(e_2,\varphi(n))=1$ to make two encryption functions:

$$\begin{align*} E_1(M)&=M^{e_1}\text{ mod }n, \text{ and } \\ E_2(M)&=M^{e_2}\text{ mod }n \end{align*}$$

When Alice puts her message into code, she double-encrypts it by calculating

$$N=E_1(E_2(M))$$

and sends $N$ to Bob. Please answer the following: a. How should Bob decrypt the message he receives from Alice? b. Suppose, by mistake, Alice calculates $N'=E_2(E_1(M))$ and, unbeknownst to Bob, sends $N'$ instead of $N$ to him. What will happen when Bob decrypts $N'$? c. How much harder is it, using this double-encryption method, for Eve to decrypt Alice's message (compared to standard single encryption).

The weight of proteins or nucleic acids in solution is commonly determined by UV spectroscopy using the Beer-Lambert law. For example, the $\mathcal{E}$ of double-stranded DNA at 260 nm is 6670 $M^{-1} \mathrm{cm}^{-1}$. The formula weight of the repeating unit in DNA (650 Daltons on average) can be used as the molecular weight. What is the weight of DNA in 2.0 mL of aqueous buffer if the absorbance, measured in a 1-cm cuvette, is 0.75?

The reaction $\mathrm { H } _ { 2 } \mathrm { SeO } _ { 3 } ( a q ) + 6 \mathrm { I } ^ { - } ( a q ) + 4 \mathrm { H } ^ { + } ( a q ) \longrightarrow \mathrm { Se } ( s ) + 2 \mathrm { I } _ { 3 } ^ { - } ( a q ) + 3 \mathrm { H } _ { 2 } \mathrm { O } ( l )$ was studied at $0 ^ { \circ } \mathrm { C } ,$ and the following data were obtained:

$$\begin{matrix} \text{$[ \mathrm { H } _ { 2 } \mathrm { SeO } _ { 3 } ] _ { 0 }$} & \text{$[ \mathrm { H } ^ { + } ] _ { 0 }$} & \text{$[ \mathrm { I } ^ { - } ] _ { 0 }$} & \text{Initial Rate}\\ \text{$( \mathrm { mol } / \mathrm { L } )$} & \text{$( \mathrm { mol } / \mathrm { L } )$} & \text{$( \mathrm { mol } / \mathrm { L } )$} & \text{$($ mol $ \mathrm {L} ^ { - 1 } \mathrm {s} ^ { - 1 })$}\\ \hline \text{$1.0 \times 10 ^ { - 4 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$1.66 \times 10 ^ { - 7 }$}\\ \text{$2.0 \times 10 ^ { - 4 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$3.33 \times 10 ^ { - 7 }$}\\ \text{$3.0 \times 10 ^ { - 4 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$4.99 \times 10 ^ { - 7 }$}\\ \text{$1.0 \times 10 ^ { - 4 }$} & \text{$4.0 \times 10 ^ { - 2 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$6.66 \times 10 ^ { - 7 }$}\\ \text{$1.0 \times 10 ^ { - 4 }$} & \text{$1.0 \times 10 ^ { - 2 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$0.42 \times 10 ^ { - 7 }$}\\ \text{$1.0 \times 10 ^ { - 4 }$} & \text{$2.0 \times 10 ^ { - 2 }$} & \text{$4.0 \times 10 ^ { - 2 }$} & \text{$13.2 \times 10 ^ { - 7 }$}\\ \text{$1.0 \times 10 ^ { - 4 }$} & \text{$1.0 \times 10 ^ { - 2 }$} & \text{$4.0 \times 10 ^ { - 2 }$} & \text{$3.36 \times 10 ^ { - 7 }$}\\ \end{matrix}$$

These relationships hold only if there is an insignificant amount of $\mathrm {I} _ { 3 } ^ { - }$ present. What is the rate law and the value of the rate constant? $( \text {Assume that rate} = - \frac { d \left[ \mathrm { H } _ { 2 } \mathrm { SeO } _ { 3 } \right] } { d t } .)$

In the study of population dynamics one of the models for a growing but bounded population is the equation

$$\frac { d P } { d t } = P ( a - b P ),$$

where $a$ and $b$ are positive constants. Solve the DE using the fact that it is a Bernoulli equation.

Which of the following explains how Mount Everest formed? (a) The mountain formed from volcanic activity at a divergent boundary. (b) The mountain formed when two tectonic plates collided at a convergent boundary. (c) The mountain formed from volcanic activity at a convergent boundary. (d) The mountain formed as a result of an earthquake when two plates slipped past each other.

Evidence that supported the hypothesis of continental drift included fossils, land features, and (a) ocean currents (b) solar activity (c) climate data (d) presence of bacteria

A large oceanic crust collides with the edge of a continent. What will happen?

You are sailing in the South Pacific Ocean, far from any plate boundary. Looming on the horizon is a dark, broad, rounded island with sparse vegetation. A few thin flows of orange lava drip into the sea. Some smoky vapor unfurls from the center of the island. What kind of volcano is this? Explain.