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the problem is here:

Mat dst = _dst.getMat();

dst is a copy , it is not synched with _dst, as you expected. instead, you should work with _dst:

void rotate(InputArray _src, OutputArray _dst, double angle,bool bKeepOldSize = false)
{
    Mat src = _src.getMat();
    Point2f pt(src.cols/2., src.rows/2.);    
    Mat r = getRotationMatrix2D(pt, angle, 1.0);
    Size ImgSize = Size(src.cols, src.rows);

    //Calculate the new image size if required
    cv::Rect bbox = cv::RotatedRect(pt,src.size(), angle).boundingRect();
    if(bKeepOldSize == false)
    {
        // adjust transformation matrix and destination matrix
        r.at<double>(0,2) += bbox.width/2.0 - pt.x;
        r.at<double>(1,2) += bbox.height/2.0 - pt.y;
        ImgSize = bbox.size();
        _dst.create(ImgSize,src.type());     // allocate larger Mat here
    }
    // pass it to warpAffine:
    warpAffine(src, _dst, r, ImgSize,INTER_LANCZOS4,BORDER_CONSTANT,Scalar(0));
}

// test code:
int main()
{
    Mat letters = imread("deskew.jpg",0);
    threshold(letters,letters,128,255,CV_THRESH_BINARY);

    Mat output;
    rotate(letters,output,-8.0);

    imwrite("output.png",output);
    cerr << output.size() << endl;
    return 0;
}
// cönsöle output:
[676 x 379]