1. Who protect our country from them?

1-2. Who protects our country from them?

(Which one is correct? Are both grammatical?)

2. There is a book shop at the corner.
2-1. There is a bookshop at the corner.
(Which one is right?)

3. Jenny is a female name, and Terry is a male name, aren't they?

4. I don't find any beauty shop in that building.
4-1. I can't find any beauty shop in that building.
(Which one is a common expression? Is #4 used commonly? Are both the same?)

5. Do you know about the movie "The Matrix"? What is the meaning of 'matrix' here?

For the first set, the second one is correct. For number three, the correct scentence is: Jenny is a female name; and Terry is a male name. Aren't they?

For number 4, the second one is correct.
For number five the meaning of matrix is the title of a movie.

Both book shop and bookshop are used.

In #4 both are used.

Here is a definition of matrix:
"1 : something within or from which something else originates, develops, or takes form " It is from the Latin Mater or mother. In the movie by that name, something originates from something else.

1. Both sentences are grammatically correct, but they have slightly different meanings.

1-1. "Who protect our country from them?" is a sentence using the plural form of "protect." It suggests that there are multiple people or entities who protect our country from something or someone.

1-2. "Who protects our country from them?" is a sentence using the singular form of "protect." It suggests that there is one person or entity who is responsible for protecting our country from something or someone.

The choice between the plural and singular forms depends on the intended meaning and context of the sentence.

2. Both sentences are grammatically correct; however, the difference lies in the spelling of "book shop" or "bookshop."

2-1. "There is a bookshop at the corner." This sentence uses the compound word "bookshop," which means a shop that sells books.

2-2. "There is a book shop at the corner." This sentence uses "book shop" as two separate words, indicating that there is a shop where books are sold at the corner.

The choice between using the compound word or separate words may depend on the customary or preferred usage in a particular region or context.

3. Yes, Jenny is generally considered a female name, while Terry is often considered a male name. However, it's important to note that names can be unisex, meaning they can be used for both genders. Ultimately, the gender association of a name may vary depending on cultural and personal preferences.

4. Both sentences are correct, but they convey slightly different nuances.

4-1. "I don't find any beauty shop in that building." This sentence suggests that the speaker is currently searching for a beauty shop in the building but is not successful in finding one.

4-2. "I can't find any beauty shop in that building." This sentence conveys the same meaning as the previous sentence but uses the contraction "can't" instead of "do not."

Both expressions are commonly used, and the choice between them depends on personal preference and the desired tone of the sentence.

5. In the movie "The Matrix," the term "matrix" refers to a computer-simulated reality that humans are unknowingly living in. It is a complex system created and controlled by machines. The word "matrix" can also refer to a concept or framework in various fields, such as mathematics or biology, where it represents a grid or structure of elements.