diff --git a/0421.py b/0421.py
new file mode 100644
index 0000000..718a632
--- /dev/null
+++ b/0421.py
@@ -0,0 +1,82 @@
+s = "Hello"
+for char in s:
+    print(f"'{char}' 的ASCII码: {ord(char)}")
+print(f"ASCII码65对应的字符: {chr(65)}")
+import math
+
+# 定义向量
+A = [3, 4]
+B = [1, 2]
+
+# 1. 计算 A + B（对应元素相加）
+A_plus_B = [A[0] + B[0], A[1] + B[1]]
+print("=== 题目3 计算结果 ===")
+print(f"1. A + B = {A_plus_B}")
+
+# 2. 计算 2 × A（数乘向量，每个元素乘系数）
+two_times_A = [2 * A[0], 2 * A[1]]
+print(f"2. 2 × A = {two_times_A}")
+
+# 3. 计算 A 的长度（模），公式：||A|| = √(x² + y²)
+A_norm = math.sqrt(A[0] ** 2 + A[1] ** 2)
+print(f"3. A 的长度（模） = {A_norm}")
+import math
+
+# 定义向量
+A = [3, 4]
+B = [1, 2]
+
+# 1. 计算 A + B（对应元素相加）
+A_plus_B = [A[0] + B[0], A[1] + B[1]]
+print("=== 题目3 计算结果 ===")
+print(f"1. A + B = {A_plus_B}")
+
+# 2. 计算 2 × A（数乘向量，每个元素乘系数）
+two_times_A = [2 * A[0], 2 * A[1]]
+print(f"2. 2 × A = {two_times_A}")
+
+# 3. 计算 A 的长度（模），公式：||A|| = √(x² + y²)
+A_norm = math.sqrt(A[0] ** 2 + A[1] ** 2)
+print(f"3. A 的长度（模） = {A_norm}")
+# 题目1
+print("=== 题目1 ===")
+s = "Hello"
+for char in s:
+    print(f"'{char}' 的ASCII码: {ord(char)}")
+print(f"ASCII码65对应的字符: {chr(65)}")
+
+# 题目3
+print("\n=== 题目3 ===")
+A = [3, 4]
+B = [1, 2]
+# 1. A+B
+A_plus_B = [A[0]+B[0], A[1]+B[1]]
+print(f"A + B = {A_plus_B}")
+# 2. 2*A
+two_A = [2*A[0], 2*A[1]]
+print(f"2 * A = {two_A}")
+# 3. A的模
+import math
+A_norm = math.sqrt(A[0]**2 + A[1]**2)
+print(f"A的长度(模) = {A_norm}")
+
+# 题目4
+print("\n=== 题目4 ===")
+A = [1, 2, 3]
+B = [4, 5, 6]
+# 1. 点积
+dot_product = sum(a*b for a,b in zip(A,B))
+print(f"A·B = {dot_product}")
+# 2. 余弦相似度
+A_norm = math.sqrt(sum(a**2 for a in A))
+B_norm = math.sqrt(sum(b**2 for b in B))
+cos_sim = dot_product / (A_norm * B_norm)
+print(f"余弦相似度 = {cos_sim:.4f}")
+# 3. A=[0,1], B=[0,1]的余弦相似度
+A2 = [0, 1]
+B2 = [0, 1]
+dot_product2 = sum(a*b for a,b in zip(A2,B2))
+A2_norm = math.sqrt(sum(a**2 for a in A2))
+B2_norm = math.sqrt(sum(b**2 for b in B2))
+cos_sim2 = dot_product2 / (A2_norm * B2_norm)
+print(f"A=[0,1], B=[0,1]的余弦相似度 = {cos_sim2}")
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