JackieLin0123/SciTikZ-Bench huggingface dataset:
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A Bosnian farmer in a non-Croat majority region wants to calculate the area of his triangular plot of land. The plot's vertices are located at the following coordinates: A(2, 1), B(8, 3), and C(5, 7). Calculate the area of this triangular plot using coordinate geometry.

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    A cricket training facility has 6 stations for different exercises, represented by nodes A, B, C, D, E, and F in the graph above. The edges represent paths between stations, with weights indicating the distance in meters. As a fitness trainer, you need to design the shortest possible circuit that visits all stations exactly once and returns to the starting point. What is the length of this optimal circuit?
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        \contour{bgcolor}{In the botanical garden, there's an irregularly shaped plot dedicated to rare medicinal herbs. The plot can be approximated as a quadrilateral with sides of 15 meters, 12 meters, 18 meters, and 20 meters. If the angle between the 15-meter and 12-meter sides is 60°, and the angle between the 18-meter and 20-meter sides is 75°, find the area of this plot to the nearest square meter.}

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As a psychologist studying the effects of social interaction on human behavior, you're modeling the spread of a viral video through a social network. The function 
\[f(t) = \frac{10000t}{t^2 + 20}\] 
represents the number of people who have viewed the video after $t$ hours. At what time $t$ (in hours) will the video reach its maximum spread rate?

\vspace{1em}

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A diplomat is tasked with allocating international aid resources among three countries: A, B, and C. The aid effectiveness function for each country is given by:

\begin{align*}
f_A(x) &= 20\ln(x+1) \\
f_B(x) &= 15\sqrt{x} \\
f_C(x) &= 25(1-e^{-0.1x})
\end{align*}

where $x$ is the amount of aid (in millions of dollars) allocated to each country, and $f(x)$ represents the impact of the aid in arbitrary units. If the total aid budget is \$30 million, how should the diplomat allocate the resources to maximize the total impact across all three countries?
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A solar energy consultant is determining the optimal angle for solar panel installation in a city located at latitude 40°N. The panels need to be tilted to maximize solar energy collection throughout the year. Given that the optimal tilt angle is approximately equal to the latitude of the location, calculate the angle $\theta$ between the solar panel and the horizontal roof surface. Round your answer to the nearest degree.

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In a tensor analysis of EEG signal propagation, you're studying the electrical potential distribution across the scalp. Given a second-order tensor $\mathbf{T}$ representing the conductivity of the scalp tissue:

\[\mathbf{T} = \begin{bmatrix}
2 & 1 & 0 \\
1 & 3 & -1 \\
0 & -1 & 4
\end{bmatrix}\]

and a gradient vector of the electrical potential $\nabla V = [2, -1, 3]^T$, calculate the magnitude of the current density vector $\mathbf{J}$ using Ohm's law in tensor form: $\mathbf{J} = -\mathbf{T}\nabla V$.
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    As an artisan selling handmade Egyptian crafts, you want to create a unique vase inspired by ancient Egyptian designs. You decide to use parametric equations to describe the shape of the vase. The equations for the vase's profile are given by:

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    $y(t) = 4 \sin(t)$
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    Where $t$ is the parameter ranging from 0 to $\pi$. Determine the shape of this Egyptian-inspired vase and sketch its profile.

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An oil spill has occurred off the coast of Aberdeen, Scotland. Environmental scientists are tracking its dispersion using vector diagrams. The initial velocity of the oil slick is 2 km/h due east. After 3 hours, a strong wind changes the direction of the slick, adding a velocity component of 1.5 km/h due north. Calculate the final displacement of the oil slick after a total of 5 hours from the initial spill.

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\textcolor{questioncolor}{A Czech film studio's production costs $C(t)$ (in millions of Czech Koruna) for a new historical drama series are modeled by the differential equation:}

\begin{equation*}
\frac{d^2C}{dt^2} + 4\frac{dC}{dt} + 3C = 10e^{-t}
\end{equation*}

\textcolor{questioncolor}{with initial conditions $C(0) = 2$ and $C'(0) = 1$, where $t$ is time in months.}

\vspace{0.5cm}

\textcolor{questioncolor}{As an exasperated film industry analyst, determine the production costs $C(t)$ using Laplace transforms. Express your answer in terms of $t$.}

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In the entertainment industry network, you have a graph representing connections between six key professionals: a talent agent, a producer, a director, an actor, a lawyer, and a publicist. The adjacency matrix A of this graph is given by:

\[A = \begin{bmatrix}
0 & 1 & 1 & 1 & 1 & 0 \\
1 & 0 & 1 & 1 & 0 & 1 \\
1 & 1 & 0 & 1 & 0 & 0 \\
1 & 1 & 1 & 0 & 1 & 1 \\
1 & 0 & 0 & 1 & 0 & 1 \\
0 & 1 & 0 & 1 & 1 & 0
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Calculate the spectral radius of this graph.
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Consider a communication network for a multicultural IT team with 4 members. The adjacency matrix $A$ representing their connectivity is given by:

\vspace{0.5em}
\[\setlength{\arraycolsep}{5pt}
A = \begin{bmatrix}
0 & 1 & 1 & 0 \\
1 & 0 & 1 & 1 \\
1 & 1 & 0 & 1 \\
0 & 1 & 1 & 0
\end{bmatrix}\]

\vspace{0.5em}
Calculate the largest eigenvalue of this matrix and interpret its significance for team connectivity optimization.
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\Large\textcolor{customblue}{\textbf{Conservation Area Rotation System}}

\vspace{0.5cm}

\normalsize
A conservation area implements a rotation system for managing different zones. The system is represented by the permutation group $G = \{e, (1234), (13)(24), (1432)\}$, where each number represents a specific zone. Identify all cyclic subgroups of $G$ and their generators.

\vspace{0.5cm}

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\begin{scope}[shift={(0,-1)}]
\foreach \i in {0,...,4}
    \foreach \j in {0,...,4}
    {
        \pgfmathparse{Mod(\i+\j,2)==0 ? "gray!30" : "white"}
        \edef\color{\pgfmathresult}
        \fill[color=\color] (\i*\squaresize,\j*\squaresize) rectangle +(\squaresize,\squaresize);
        \draw[BurntOrange, thick] (\i*\squaresize,\j*\squaresize) rectangle +(\squaresize,\squaresize);
    }
\end{scope}

\node[text width=10cm, align=justify, font=\small] at (2.5,-2.5) {
Consider the 5x5 quilt pattern shown above, composed of alternating light and dark squares. How many lines of symmetry does this pattern have?
};

\end{tikzpicture}

\end{document}
\documentclass[border=10pt]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=0.04]
\draw[thick,orange!80!black] (0,0) -- (120,40) -- (100,100) -- (60,120) -- (20,80) -- cycle;
\fill[orange!20] (0,0) -- (120,40) -- (100,100) -- (60,120) -- (20,80) -- cycle;
\foreach \point in {(0,0), (120,40), (100,100), (60,120), (20,80)}
    \fill[red] \point circle (3pt);
\node[anchor=north east] at (0,0) {(0, 0)};
\node[anchor=north west] at (120,40) {(120, 40)};
\node[anchor=west] at (100,100) {(100, 100)};
\node[anchor=south] at (60,120) {(60, 120)};
\node[anchor=east] at (20,80) {(20, 80)};
\end{tikzpicture}
\end{document}
\documentclass[border=10pt]{standalone}
\usepackage{amsmath,amssymb,tikz,xcolor}
\usepackage[most]{tcolorbox}

\definecolor{customblue}{RGB}{70,130,180}
\definecolor{custompink}{RGB}{255,182,193}

\begin{document}

\begin{tcolorbox}[
    enhanced,
    colback=custompink!10,
    colframe=customblue,
    boxrule=1pt,
    arc=5mm,
    fontupper=\large\color{customblue},
    fonttitle=\bfseries\color{white},
    title=Coffee Shop Queue Optimization,
    attach boxed title to top center={yshift=-2mm},
    boxed title style={
        size=small,
        colback=customblue,
        rounded corners
    }
]
As a barista managing a busy coffee shop, you've decided to use your experience with arcade cabinet layouts to optimize your queue system. You set up a 2D coordinate system where the coffee counter is at (0, 0), and each unit represents 1 meter. Customers form a zigzag queue starting at (1, 0), then (1, 1), (2, 1), (2, 2), and so on.

If your shop can accommodate a maximum queue length of 10 meters before reaching the door, what are the coordinates of the last customer in the queue, and how many customers can be in the queue?

\begin{center}
\begin{tikzpicture}[scale=0.7]
\draw[thick,->] (0,0) -- (6,0) node[right]{x};
\draw[thick,->] (0,0) -- (0,6) node[above]{y};
\fill[customblue] (0,0) circle (3pt) node[below left] {Counter (0,0)};
\foreach \i in {0,...,5} {
    \fill[custompink] (\i,\i) circle (2pt);
    \fill[custompink] (\i+1,\i) circle (2pt);
    \if\i5\else
        \draw[->,thick,customblue] (\i,\i) -- (\i+1,\i);
        \draw[->,thick,customblue] (\i+1,\i) -- (\i+1,\i+1);
    \fi
}
\node[above right] at (5,5) {Door};
\end{tikzpicture}
\end{center}

\end{tcolorbox}

\end{document}
\documentclass[border=10pt]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=0.025]
\draw[thick] (0,0) ellipse (100 and 80);
\draw[-stealth,thick] (-100,0) -- (100,0) node[right] {200 m};
\draw[-stealth,thick] (0,-80) -- (0,80) node[above] {160 m};
\fill (0,0) circle (2);
\end{tikzpicture}
\end{document}