Merge commit 'e5d82c06'

题库0.3/Problems.json

@@ -3651,7 +3651,7 @@
     },
     "000137": {
         "id": "000137",
-        "content": "如图, 有一块边长为$3\\text{m}$的正方形铁皮$ABCD$, 其中阴影部分$ATN$是一个半径为$2\\text{m}$的扇形. 设这个扇形已经腐蚀不能\n使用, 但其余部分均完好. 工人师傅想在未被腐蚀的部分截下一块其边落在$BC$与$CD$上的矩形铁皮$PQCR$, 使点$P$在弧$TN$上. 设$\\angle TAP=\\theta$, 矩形$PQCR$的面积为$S\\text{m}^2$.\n\\begin{center}\n    \\begin{tikzpicture}\n        \\begin{scope}[even odd rule]\n            \\clip (0,0) rectangle (3,3) (0.55,0.15) circle (0.15);\n            \\fill [gray!30] (0,0) -- (2,0) arc (0:90:2) -- cycle;\n        \\end{scope}\n\n        \\draw [thick] (0,0) node [below left] {$O$} -- (3,0) node [below right] {$B$} -- (3,3) node [above right] {$C$} -- (0,3) node [above left] {$D$} -- cycle;\n        \\draw [thick] (0,0) -- (40:2) node [above right] {$P$} -- (3,{2*sin(40)}) node [right] {$Q$} (40:2) -- ({2*cos(40)},3) node [above] {$R$};\n        \\draw [thick] (0,0) -- (2,0) node [below] {$T$} arc (0:90:2) node [left] {$N$} -- cycle;\n        \\draw (0.4,0) arc (0:40:0.4) (0.55,0.15) node {$\\theta$};\n    \\end{tikzpicture}\n\\end{center}\n(1) 求$S$关于$\\theta$的函数表达式;\\\\\n(2) 求$S$的最大值及$S$取得最大值时$\\theta$的值.",
+        "content": "如图, 有一块边长为$3\\text{m}$的正方形铁皮$ABCD$, 其中阴影部分$ATN$是一个半径为$2\\text{m}$的扇形. 设这个扇形已经腐蚀不能\n使用, 但其余部分均完好. 工人师傅想在未被腐蚀的部分截下一块其边落在$BC$与$CD$上的矩形铁皮$PQCR$, 使点$P$在弧$TN$上. 设$\\angle TAP=\\theta$, 矩形$PQCR$的面积为$S\\text{m}^2$.\n\\begin{center}\n    \\begin{tikzpicture}\n        \\begin{scope}[even odd rule]\n            \\clip (0,0) rectangle (3,3) (0.55,0.15) circle (0.15);\n            \\fill [gray!30] (0,0) -- (2,0) arc (0:90:2) -- cycle;\n        \\end{scope}\n\n        \\draw [thick] (0,0) node [below left] {$A$} -- (3,0) node [below right] {$B$} -- (3,3) node [above right] {$C$} -- (0,3) node [above left] {$D$} -- cycle;\n        \\draw [thick] (0,0) -- (40:2) node [above right] {$P$} -- (3,{2*sin(40)}) node [right] {$Q$} (40:2) -- ({2*cos(40)},3) node [above] {$R$};\n        \\draw [thick] (0,0) -- (2,0) node [below] {$T$} arc (0:90:2) node [left] {$N$} -- cycle;\n        \\draw (0.4,0) arc (0:40:0.4) (0.55,0.15) node {$\\theta$};\n    \\end{tikzpicture}\n\\end{center}\n(1) 求$S$关于$\\theta$的函数表达式;\\\\\n(2) 求$S$的最大值及$S$取得最大值时$\\theta$的值.",
         "objs": [
             "K0320003B",
             "K0320002B",