is skew supposed to move/shift top/left x?

When skewing in the x direction, top x seems to move to the right a bit.I
have attached a png. The red rectangle is not skewed, while the black is
skewed at 45. The skewed (black) rectangle looks shifted to the right a few
pixels. That is the top is not aligned. I would think there should be a
diagonal line cutting through the top left hitting the bottom right corner.
From my past history, I am probably doing something wrong. Thanks in
advance.

#include <cairo.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>

/*
http://cairographics.org/cookbook/matrix_transform/http://cairographics.org/cookbook/matrix_transform/
Lets take that C = math.cos(A), S = math.sin(A), T = math.tan(A)
X-skew by A    --    mtrx = cairo.Matrix(1,0,T,1,0,0)
Y-skew by A    --    mtrx = cairo.Matrix(1,T,0,1,0,0)
*/

int
main (int argc, char *argv[])
{
  cairo_surface_t* cs;
  cairo_t *cr;
  double angle;
  double skewx;
  cairo_matrix_t matrix;

  cs= cairo_image_surface_create(CAIRO_FORMAT_ARGB32, 130.,100.);
  cr= cairo_create(cs);

  cairo_set_source_rgb(cr, 1., 0., 0.);
  cairo_rectangle(cr, 10., 10., 50., 50.);
  cairo_stroke(cr);

  angle= 45.;
  skewx= tan(angle * M_PI / 180.);
  cairo_matrix_init(
      &matrix,
      1.0, 0.0,
      skewx, 1.0,
      0.0, 0.0);
  cairo_transform(cr, &matrix);
  cairo_rectangle(cr, 10., 10., 50., 50.);
  cairo_set_source_rgb(cr, 0., 0., 0.);
  cairo_stroke(cr);

  cairo_surface_write_to_png(cs, "skew.png");

  cairo_destroy(cr);
  cairo_surface_destroy(cs);

  return 0;
}

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/* 
vim:expandtab:softtabstop=2:tabstop=2:shiftwidth=2:nowrap:ruler
*/
#include <cairo.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>

/*
http://cairographics.org/cookbook/matrix_transform/http://cairographics.org/cookbook/matrix_transform/
Lets take that C = math.cos(A), S = math.sin(A), T = math.tan(A)
X-skew by A	--	mtrx = cairo.Matrix(1,0,T,1,0,0)
Y-skew by A	--	mtrx = cairo.Matrix(1,T,0,1,0,0)
*/

int
main (int argc, char *argv[])
{
  cairo_surface_t* cs;
  cairo_t *cr;
  double angle;
  double skewx;
  cairo_matrix_t matrix;

  cs= cairo_image_surface_create(CAIRO_FORMAT_ARGB32, 130.,100.);
  cr= cairo_create(cs);

  cairo_set_source_rgb(cr, 1., 0., 0.);
  cairo_rectangle(cr, 10., 10., 50., 50.);
  cairo_stroke(cr);

  angle= 45.;
  skewx= tan(angle * M_PI / 180.);
  cairo_matrix_init(
      &matrix,
      1.0, 0.0,
      skewx, 1.0,
      0.0, 0.0);
  cairo_transform(cr, &matrix);
  cairo_rectangle(cr, 10., 10., 50., 50.);
  cairo_set_source_rgb(cr, 0., 0., 0.);
  cairo_stroke(cr);

  cairo_surface_write_to_png(cs, "skew.png");

  cairo_destroy(cr);
  cairo_surface_destroy(cs);

  return 0;
}