If a variable with the same name exists in both the local and global environment in R, the local variable will be used. R follows the scoping rules where variables defined in the local environment take precedence over variables with the same name in the global environment.

To square a number in R, you use the ^ operator with 2 as the exponent. For example, to calculate the square of 4, you would use 4^2, which would return 16.

The substr() function in R is used to extract a specific substring from a string. For example, substr("Hello", 2, 3) would return "el".

If you have two character vectors in R, you can concatenate corresponding elements from each vector with a hyphen in between using the 'paste()' function with 'sep = "-"'. For example, 'paste(c("Hello", "Goodbye"), c("world!", "friends!"), sep = "-")' would return a vector containing "Hello-world!" and "Goodbye-friends!".

To create a pie chart in R that color-codes segments based on a specific criteria, you would use the pie() function. Provide a vector of colors corresponding to each segment, ensuring that the colors align with the specific criteria you want to represent.

To calculate the mode of a numeric vector in R, you would need to define a custom function. Since R does not have a built-in function for mode, you can create a custom function that uses appropriate logic to identify the mode based on the frequency of values.

Performance optimization in R often involves identifying bottlenecks (Rprof() can help with this), using more efficient data structures (like data.table), and vectorizing operations. If the task is highly computational and the system has multiple cores, using parallel processing might also help speed up the execution.

The mean() function is commonly used to calculate the mean (average) of a numeric vector in R. It returns the arithmetic mean of the values.

Recursive functions in R can be used to solve problems that have a self-similar structure. These are problems where a solution to a larger instance of the problem can be obtained by combining solutions to smaller instances of the same problem. The recursive function breaks down the problem into smaller sub-problems, solving them recursively until a base case is reached. This self-similar structure allows for the application of recursion to efficiently solve the problem.

In R, the det() function can be used to compute the determinant of a matrix. The det() function takes a matrix as its argument and returns its determinant. The determinant is a value that provides information about the invertibility and properties of the matrix.