determinants的音標是[d??t??m?n?nts]，基本翻譯為“決定因素，決定力”。

速記技巧：使用發音類似的字母或符號來記憶單詞。可以將determinants拆分為“de-ter-mi-nants”，其中de-表示“決定”，ter-mi-n表示“結束”，-ant表示“……的”，所以可以理解為“決定因素”。

請注意，以上內容僅供參考，因為學習語言需要不斷練習和實踐。如果需要更多信息，可以請教英語老師或查閱相關書籍。

Determinants 的詞源：

詞根：determinant

詞源：來自拉丁語 determinant，意為“決定性的”。

變化形式：

過去式：determined

過去分詞：determined

現在分詞：determining

復數：determinants

相關單詞：

1. Determinate - 決定性的，明確的

2. Indeterminate - 不確定的，模糊的

3. Determinism - 決定論，認為一切由因果關系決定

4. Determinate Number - 決定數，確定性數

5. Determinate Equation - 決定性方程，有解的方程

6. Determinate Boundary - 決定性邊界，有解的邊界條件

7. Determinate Calculus - 確定論微積分

8. Determinate Projection - 確定投影

9. Determinate Solution - 確定解，有解的解

10. Determinate System - 確定系統，有解的系統

常用短語：

1. determinant of a matrix

2. determinant of a system of equations

3. sign of a determinant

4. absolute determinant

5. minor of a determinant

6. determinant of a square matrix

7. determinant of a linear transformation

雙語例句：

1. The determinant of a 2x2 matrix can be found easily using the formula. （一個2x2矩陣的行列式可以通過公式很容易地求出。）

2. The determinant of a system of equations determines the solution set. （方程組的行列式決定了解集。）

3. The sign of a determinant can sometimes indicate the direction of the solution. （行列式的符號有時可以指示解的方向。）

4. The absolute value of a determinant gives the magnitude of the solution. （行列式的絕對值給出了解的幅度。）

5. Minors of a determinant can be used to solve systems of equations efficiently. （行列式的次級可以用來有效地解決方程組。）

6. Determinants are used in linear transformations to determine the eigenvectors and eigenvalues. （在線性變換中，行列式用于確定特征向量和特征值。）

7. Determinants are an essential tool in mathematical analysis and physics. （行列式是數學分析和物理學中不可或缺的工具。）

英文小作文：

Determinants are an essential tool in mathematics that help us solve equations and systems of equations efficiently. They are also used in linear transformations to determine eigenvectors and eigenvalues, which are important concepts in mathematical physics and engineering. However, determinants can be tricky to understand, especially when dealing with higher-dimensional matrices and systems of linear equations. Understanding determinants requires a careful examination of their properties and formulas, as well as an understanding of how they relate to other mathematical concepts such as vectors and matrices. Despite their complexity, determinants are an indispensable tool in many fields of mathematics and science, and they continue to fascinate mathematicians and students alike with their beauty and power.