新增两道关联题

题库0.3/Problems.json

@@ -34183,7 +34183,9 @@
         "same": [
             "011334"
         ],
-        "related": [],
+        "related": [
+            "024613"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -498751,7 +498753,9 @@
             "20230705\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024614"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -668391,6 +668395,63 @@
         "space": "4em",
         "unrelated": []
     },
+    "024613": {
+        "id": "024613",
+        "content": "在平面直角坐标系$xOy$中, 将点$A(2,1)$绕原点$O$逆时针旋转$\\dfrac\\pi 4$到点$B$, 若以射线$OB$为终边的角为$\\alpha$, 则$\\cos \\alpha$的值为\\blank{50}.",
+        "objs": [
+            "K0701001X"
+        ],
+        "tags": [
+            "第七单元",
+            "直线",
+            "2023届高三-四月错题重做-04-易错题-解析几何",
+            "2023届高三-四月错题重做-04-解析几何",
+            "2023届高三-第一轮复习讲义-34-直线及其方程",
+            "J20240534-第一轮复习讲义34直线及其方程"
+        ],
+        "genre": "",
+        "ans": "$\\frac{\\sqrt{10}}{10}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "赋能练习-20240226修改",
+        "edit": [
+            "20220624\t朱敏慧, 王伟叶",
+            "20240226\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000960"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024614": {
+        "id": "024614",
+        "content": "已知角$\\alpha$满足$\\sqrt{3} \\sin \\alpha+\\cos \\alpha=1$, 求$\\alpha$的值的集合.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第二册三角例题与习题-20240226修改",
+        "edit": [
+            "20230705\t王伟叶",
+            "20240226\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "018388"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",